I'm going to propose Analog 8 as your anthology. Published in 1971, cover shown in the link.
I base this identification on the first story you mention, about space fighter-pilots enclosed in womb-like structures. I've read it, and will list the details I managed to find. It's "Womb to Tomb" by Joseph Wesley, also known as L. J. Stecher. Originally published in Analog August 1969. According to ISFDB, to which the above links point, it has been anthologised in Analog 8.
It has also been published in Best SF: 1969 edited by Harry Harrison and Brian Aldiss. This also appeared under the title The Year's Best Science Fiction No. 3. The latter is the British version of the book, and is almost certainly where I first read "Womb to Tomb"
I couldn't find an online copy of "Womb to Tomb". However, I did find a summary of a French translation, "La Première et dernière demeure", published in Histoires de guerres futures edited by Jacques Goimard. That was enough to confirm that it is the story I was thinking of. Here's an English translation of that summary:
Admiral Burkens, head of the Functional Re-education Centre for Combat-Injured Spacecraft Pilots, receives a visit from Senator Grimes. Grimes comes to enquire about his son Jim, wounded in combat against the Kwartah with whom humanity is fighting a long and bitter war.
Burkens tells Grimes about a combat vehicle, “the Egg”, which makes pilots much more efficient. The pilot is immersed in an airtight capsule, filled with a liquid which both nourishes them and provides them with air [or at least oxygen, probably under pressure]. The Egg is equipped with extremely resilient armour and sophisticated means of protection (and, notably, can act as a lifeboat), and has proven very effective, enabling its pilot to stay permanently in combat.
The downside is that the pilot gets so used to his Egg that he no longer wants to come out, like a child who wishes to remain in the maternal amniotic fluid. So you might say that The Egg has become the soldier's first abode, as if he were still unborn, but will probably also be his last. Forcibly removing the pilot from his "womb" causes trauma equivalent to that of a Caesarean section, after which he goes cataleptic and regresses to the mental state of an infant.
And so the Centre's job is to rehabilitate thousands of pilots. Studies show that it is only safe to leave the Egg three times: a fourth exit causes such "psychological loss" that it should only be risked in the event of an extreme emergency (such as a massive attack by the enemy). This is why, after three exits from the Egg, one is re-deployed to the rear as logistical support. That's what happened to Jim. So Senator Grimes can be assured that no matter how much his son begs, threatens or yells, he will never return to an Egg.
Burkens finishes by explaining that this was his own situation too. The story ends with this last sentence from him: “God! How I wish the Kwartah would attack us now!"
So that confirms "Womb to Tomb". This Goodreads discussion confirms that I saw it in The Year's Best Science Fiction No. 3. User Roddy Williams gave summaries of all the stories there. "Womb to Tomb" matches, and so do the others.
The reason I suggest that you saw "Womb to Tomb" in Analog 8 is that none of the The Year's Best Science Fiction No. 3/Best SF: 1969 contents seem to match the second story you describe, about the boy living alone in a house controlled by a house "nanny" computer after an atomic war. And ISFDB lists Analog 8 as the only other anthologiser.
Having said that, I'm not really convinced by Analog 8 either, as I'm not sure the titles of the stories in it would fit with a boy living alone etc. But at least I hope identifying "Womb to Tomb" helps you track down your anthology.