1) Critically depends on answer 3, but I would say yes anyway. A bare tank is said to be more stressful to fauna as there is a lot of reflections which spook them out. Not many plants will grow without a good foothold in some sort of substrate, and you will have to forget about any sort of "design" to the layout without
gravel, as plants would be constantly being moved by the fauna. As mentioned about answer three... the gravel (especially if small, irregular grains) will be a big surface area for bacteria to develop which "filter" the toxins in the water by converting ammonia, to nitrites, then nitrates. Therefore, without a filter to do most of the work for you, the gravel will become the next major source of biological filtration.
2) It really depends on how much light the tank will recieve, but you can go for the easy, low-light plants such as java moss, java fern, anubias etc that will at least give you an indication of light levels in their growth.... they will tollerate and grow in dull condtions, but will show greater growth if higher light is available.
3) I would say it depends how heavily planted the tank will be, and how much you want to experiment. Here is a pic of my 6 gallon tank that is probably more like 3 or 4 after displacement from large pieces of bogwood...
I have no filter on that, and current inhabitants are three large adult African dwarf frogs, 1 sparkling gourami and a large (approx 2.5") wood shrimp. Plants are labelled, and I wouldn't exactly call it heavily planted!
I have no problems with water quality on this tank and actually have to add nitrates every three to four days (at a level of 15ppm) as they dissapear! You can always add some duckweed (lemna minor) to your tank to soak up nutrients.
This tank has also gone weeks without a water change before with no problems whatsoever (as nitrates never accumulate). Currently, I have returned to the no water change plan for a while. Last one was done on 6th March.
If you go for the no filter route, be sure to test the water at first for a while to be sure that nothing is building up too much.
4) Shrimp do not really
add much to the bioload of an aquarium, however you are talking about a small volume of water. You might be able to squeeze another smallish fish in there or a few more shrimp, but again.... water testing would indicate the answers you were looking for.
5) By peace lily, I assume you mean the common Spathiphyllum sp. which is a terrestrial plant? If so, can these grow in water? I have read that they do not like to be standing in water for any length of time.
This sort of setup can work, you just might have to fiddle a bit with it to get the right balance.
The only other thing I would mention is about the sunlight. Just make sure it does not get too much direct light (which you said it doesn't really so you should be fine), as this can cause problems by heating the water, especially such a small body like 2.5 gallons