Why did Howland Reed not send men and/or come himself to fight with Robb in the war of the 5 Kings or with Jon at the Battle of the Bastards? And why did Bran send Rickon to the Umbers and not Reed when Rickon needed to be hidden away.
Battle of the Bastards didn't happen in the books....yet.
As to your main question , Because Robb ordered Howland Reed to stay there and bleed the Lannisters if they decide to march on the North.
"If he comes so far, but no one thinks he will," Robb said. "I've sent word to Howland Reed, Father's old friend at Greywater Watch. If the Lannisters come up the Neck, the crannogmen will bleed them every step of the way, but Galbart Glover says Lord Tywin is too smart for that, and Roose Bolton agrees. He'll stay close to the Trident, they believe, taking the castles of the river lords one by one, until Riverrun stands alone. We need to march south to meet him."
AGOT- Catelyn VIII
Historical traditions of the Crannogmen
Bear in mind, this is the historic role Crannogmen have played, guarding the Southern gate of the North.
The northern boundary of the Stark domains was protected by the Wall and the men of the Night's Watch, whilst to the south, the only way through the swamps of the Neck passed below the ruined towers and sinking walls of the great fortress called Moat Cailin. Even when the Marsh Kings held the Moat, their crannogmen stood staunch against any invaders from the south, allying with the Barrow Kings, Red Kings, and Kings of Winter as need be to turn back any southron lord who sought to attack the North. And once King Rickard Stark added the Neck to his domain, Moat Cailin proved even more imposing—a bulwark against the powers of the south. Few sought to push past it, and the histories say that none ever succeeded.
TWOIAF- The North: The Kings of Winter
Liege Levies from Crannogmen
While Lord Reed was going to stay behind, he most certainly sent his levies as was his duty.
"He must march soon, or not at all," Maester Luwin said. "The winter town is full to bursting, and this army of his will eat the countryside clean if it camps here much longer. Others are waiting to join him all along the kingsroad, barrow knights and crannogmen and the Lords Manderly and Flint. The fighting has begun in the riverlands, and your brother has many leagues to go."
AGOT- Bran VI
Robb's shield and strong hand
Later when the North was overrun by Squids, it was Howland Reed Robb had pinned his hopes on. (Although it is unclear if Howland Reed ever received the missive from Robb):
"Tell Howland Reed that he is to send guides to me, two days after I have started up the causeway.
"Go upriver flying my banner. The crannogmen will find you. I want two ships to double the chances of my message reaching Howland Reed. Lady Maege shall go on one, Galbart on the second." He turned to the two he'd named.
Galbart Glover rubbed his mouth. "There are risks. If the crannogmen should fail you . . ."
"We will be no worse than before. But they will not fail. My father knew the worth of Howland Reed." Robb rolled up the map.
ASOS- Catelyn V
Another reason is, since coming back from the Rebellion, Howland Reed became a recluse. Bran noted that as well:
Finally all of the principal vassals of House Stark had been heard from save for Howland Reed the crannogman, who had not set foot outside his swamps for many a year
ACOK- Bran II
Later it was the Crannogmen and Lord Reed who carried on Northern resistance against the Ironborn:
"I beached her beneath Norne Goodbrother's castle and rode across the island." She sat upon a stool and helped herself unasked to Nute the Barber's wine. Nute raised no objection; he had passed out drunk some time ago. "Who holds the Moat?"
"Ralf Kenning. With the Young Wolf dead, only the bog devils remain to plague us."
AFFC- The Iron Captain
How did Rickon end up where he ended up?
Bran didn't decide where Rickon was gonna go. It was Maester Luwin. He told Asha that the boys should not be together and left the rest to her. That's what she did. In the books, there is rumor that Rickon is in Skagos, not in Last Hearth.
"Listen," Luwin said to Osha, "the princes . . . Robb's heirs. Not . . . not together . . . do you hear?"
The wildling woman leaned on her spear. "Aye. Safer apart. But where to take them? I'd thought, might be these Cerwyns . . ."
Maester Luwin shook his head, though it was plain to see what the effort cost him. "Cerwyn boy's dead. Ser Rodrik, Leobald Tallhart, Lady Hornwood . . . all slain. Deepwood fallen, Moat Cailin, soon Torrhen's Square. Ironmen on the Stony Shore. And east, the Bastard of Bolton."
"Then where?" asked Osha.
"White Harbor . . . the Umbers . . . I do not know . . . war everywhere . . . each man against his neighbor, and winter coming . . . such folly, such black mad folly . . ." Maester Luwin reached up and grasped Bran's forearm, his fingers closing with a desperate strength. "You must be strong now. Strong."
ACOK- Bran VII
This part is mere speculation. Given how show keeps skipping details (For many legitimate reasons), I tend to stay away from Show questions now. Will take it out once someone posts a Show-POV answer.
Bran didn't send Rickon to Greywater Watch Because the road to South was full of Ironmen. Moat Callin had fallen to the Ironborn along with many other coastal areas. Last Hearth, seat of House Umber was still safe.
As to why didn't Reed play a role in War of the Five Kings or the Battle of the Bastards, Well that's because D&D. They probably didn't think it was worth airtime.
GRRM's Position on when will Howland Reed appear
In correspondence with a fan, this is what George said:
Question 3: It had been stated that Howland Reed would come out in The Winds of Winter, which is the 5th book. Will he still come in the 5th book (A Dance with Dragon)?
Answer: He will appear eventually.
He will appear and play a more active role when George deems the time is right for, uh, the Grand revelation.
Conclusion (Books only)
- Howland Reed stayed behind personally because Robb commanded him to.
- He provided soldiers to Robb's Army when Robb called the banners.
- He is playing his part in the war very well.
- Bran had no control over Rickon's destination.
- Rickon didn't go to the Umbers.
Don't forget it is Jojen and Meera Reed, Howland's own children who are at Winterfell to help Bran and Rickon escape! At the time it was too dangerous to head south.
Howland did help Robb in the War of Five Kings:
"If he comes so far, but no one thinks he will," Robb said. "I've sent word to Howland Reed, Father's old friend at Greywater Watch. If the Lannisters come up the Neck, the crannogmen will bleed them every step of the way, but Galbart Glover says Lord Tywin is too smart for that, and Roose Bolton agrees. - A Game of Thrones - Catelyn VIII
They may not been much of a great help to a standing army with heavy armor:
They were a poor folk, fishers and frog-hunters who lived in houses of thatch and woven reeds on floating islands hidden in the deeps of the swamp. It was said that they were a cowardly people who fought with poisoned weapons and preferred to hide from foes rather than face them in open battle. - A Clash of Kings - Bran III
But they still posed a threat, especially within their own lands:
Moat Cailin sits on the edge of the bogs. Lord Howland can make your uncle's occupation a visit to hell if he chooses, but so long as you hold his heirs he must stay his hand." - A Clash of Kings - Theon IV
"There are ways through the Neck that are not on any map, Uncle. Ways known only to the crannogmen—narrow trails between the bogs, and wet roads through the reeds that only boats can follow." He turned to his two messengers. "Tell Howland Reed that he is to send guides to me, two days after I have started up the causeway. To the center battle, where my own standard flies. - A Storm of Swords - Catelyn V
So "Where is Howland Reed"... He is in his own lands aiding the North in the best way he can due to his limited resources and lack of a large army.