[RPG] Can you long/short rest during Astral Projection

Yes, you can use astral projection from planes other than the Material Plane. The Manual of the Planes describes how spells that access transitive planes such as the Astral Plane function on other planes in the section "Moving Among Transitive Planes" (starting on page 45).

Characters generally must use spells or spell-like abilities to access a Transitive Plane. ... the astral projection spell takes you to the Astral Plane ... Such spells should function in any location coexistent with or coterminous to the plane.

It includes various examples of travel between transitive planes on page 46. These examples reinforce that "Material Plane" is a placeholder and that you can use astral projection from anywhere that is connected to the astral plane. Your body will be left behind on the plane you project from.

From the Ethereal Plane to the Astral Plane: You can move to the Astral Plane from almost everywhere on the Ethereal Plane, because the Astral Plane connects to everywhere on the Ethereal Plane. ... If you're using an astral projection spell, your physical body remains in the Ethereal Plane ...

From the Plane of Shadow to the Astral Plane: From the Plane of Shadow, you can use the astral projection spell, leaving your body behind on that plane ...

You're correct.

Your analysis is correct--a warlock can cast some long-duration spells by effectively spending hours instead of spell slots.

This is not unbalanced (for a single-classed warlock).

First, the spell slots that the warlock recovers on a short rest can only go up to level 5. Any long-duration spell above level 5 is subject to Mystic Arcanum, which only allows the warlock to cast it once per long rest (as explained here).

So which spells on the list are both level 5 or less and last longer than an hour? My quick perusal through the list shows only Hallucinatory Terrain, Hex, and Dream. Dream is arguably a special case, and Hex only works on one target at a time because of concentration, so your example of Hallucinatory Terrain is essentially the only spell that can be "exploited" this way. Opinions may vary about whether this "exploit" is especially powerful or not, but given that it the spell is quite limited in scope and it requires uninterrupted rests, I'd hardly consider it to be abuse.

Multiclassed warlocks can benefit this way

As Bloodcinder points out, multiclass warlocks can use their warlock spell slots to cast spells from their other classes (PHB 164):

If you have both the Spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the Spellcasting class feature...

Thus, a warlock that has levels in wizard could cast a spell like Mage Armor, take a short rest to regain that spell slot, and then enjoy the benefits of Mage Armor for another 7 hours afterward.

As for whether this is balanced, I'd have to assume that the designers considered this possibility because the rule was written out so explicitly. After all, multiclassed spellcasters are delaying (or sacrificing) their ability to cast higher level spells, so there is some tradeoff to be considered.