There's very little information about the physical nature of the Halls of Mandos in Tolkien's writings aside from this passage on the Chaining of Melkor which I've extracted from History of Middle-earth 10 (a similar passage appears in Chapter 3 of the Silmarillion):
...the halls of Mandos, from whence none have ever escaped save by the will of Mandos and Manwe, neither Vala, nor Elf, nor mortal Man. Vast are those halls and strong, and they were built in the north of the land of Aman.
There's absolutely no evidence in Tolkien to suggest that living Elves can visit these Halls; in fact there are clear statements that suggest that the living do not mingle with the dead, for example the following passage (also from History of middle-earth 10, this time in relation to the judgement on Finwe and Miriel):
When Mandos had spoken thus, the Eldar who were present asked: 'How then shall the will or the doom be known?' It was answered: 'Only by recourse to Manwe, and by the pronouncement of Mandos. For who among the Living can discover the will of the Dead, or presume the judgements of Mandos?'
This is confirmed by a passage in the very late writings on Glorfindel given in History of Middle-earth 12:
Glorfindel remained in the Blessed Realm, no doubt at first by his own choice: Gondolin was destroyed, and all his kin had perished, and were still in the Halls of Waiting unapproachable by the living.
There is therefore no mingling of the living with the dead. But (and going into speculative territory) even if they could, the statement in my first quote above that escape from Mandos is impossible would mean that they would never get out (unless Mandos himself permitted it) to tell the living what they had seen there.
Regarding the travel of a spirit to the Halls of Mandos, there is little information, but the Finwe and Miriel material has this to say:
It was in Aman that they learned of Manwe that each fea was imperishable within the life of Arda, and that its fate was to inhabit Arda to its end. Those fear, therefore, that in the marring of Arda suffered unnaturally a divorce from their hroar remained still in Arda and in Time. But in this state they were open to the direct instruction and command of the Valar. As soon as they were disbodied they were summoned to leave the places of their life and death and go to the 'Halls of Waiting': Mandos, in the realm of the Valar.
It is of course unclear from this whether the travel is instantaneous or if there is some time between death and arrival at Mandos, but we really don't have anything more to work with. What is confirmed in following passages is that the summons to Mandos may be refused, and so we can state with certainty that Elves don't always go to the Halls of Mandos when they die.
The final consideration is the matter of those who have returned from Mandos and what they report of their time there, and again I'll quote from the Finwe and Miriel material in History of Middle-earth 10:
The Re-born report that in Mandos there are many elves, and among them many of the Alamanyar, but that there is in the Halls of Waiting little mingling or communing of kind with kind, or indeed of any one fea with another. For the houseless fea is solitary by nature, and turns only towards those with whom, maybe, it formed strong bonds of love in life.
And:
As for guilt in other matters little is known of the dealings of Mandos with the Dead. For several reasons: Because those who have done great evil (who are few) do not return. Because those who have been under the correction of Mandos will not speak of it, and indeed, being healed, remember little of it; for they have returned to their natural courses...
From this we get confirmation (which also exists elsewhere) that return from Mandos is not always guaranteed, and that those who do return have little enough to report.
