Optimizing mesh for the game (in 3DS Max)

Yes it is fine to leave the meshes like that. It will be triangulated later by itself.

As for the uv. If you change the sice you need to scale the uv in the x axis in the uv map editor after you change the size. Or as it is a simple map you can re-do it after changing the size. I don't know what mapping mode did you use. I think a planar map will be the correct one. Since that map looks a little wonky.

Ah someone that works with 3ds max like I do :D
That mesh is fine honey, for the UV map the map seems to look ohkayy, but heres what I do when im UV mapping and my textures usually come out nice.
First, I use the unwrap UV modifer like you do, then I mark seams. I use the point to point seam tool (I forgot the exact name) But it should be in the same space as that Green line tool, and then I use vertice selection, to make a seam.
Heres a video explaining pretty much exactly what I do
Use either a 2048x2048 map or a 1024x1024 map. Do not make your mesh originally to the Sims 4 texture map, I usually do this because I make my meshes for both sims 3 and 4 usually, and if I want to render I usually use the better textures, as sims 4 texture map space, especially for acessories is soooo tiny.
So jus resize your uvs according to one of the standards. Then when you finish your mesh, collapse all modifiers and Export it as a .obj. Also if you want you can bake the textures in 3ds max because Mental Ray is awesome. You'll just have to create a studio, make some lights assign materials etc. I personally have switched to Vray but I used to use mental ray and use the default 3ds max Studio as my place to bake out materials.
When you do that, import it to blender, then you can resize your UV, and if you baked your textures in 3ds max you can resize them down in photoshop and sharpen them.
Of course you can just scale it alon the sims 4 texture map in 3ds max, Just import a image of the sims 4 texture map, and make it super small to fit the appropriate texture space. Then you can bake your textures like that as well, however you won't be able to scale the bake up without it blurring a lot, so importing to other games is kinda out of the question, unless you make new textures, but its up to you! I just always like to have the original 1k or 2k textures for future projects. (Skyrim, Secondlife, IMVU, Daz Studio, etc.)

inabadromance thank you for clearing this up! I think I read somewhere that studio triangulates meshes and that the mesh has to be triangulated but it didn't settle in my mind.
I tried that preferences that you wrote about but it doesn't work. I think it's for different purposes when texture is small and object is very big. When you assign small texture to the big object texture looks very blurry. So I think it's for this purpose (want to try later because it will be a solution for another little problem for me).

Mathcope I used Unwrap UVW -> Edit UV. I think it's the only modificator to work on uv layout directly, all other just help to unwrap the texture in different ways. I scaled down the texture, just wanted to know may be it's somewhere in preferences and I don't know about it.

orangemittens that's super convenient . Thank you! Because I've been tweaking it for hours trying to figure out how to triangulate this object the same way that it looks in studio. Learning the program step by step. It's a lot to learn.

eliavah thank you for explanation! I love that method with marking seems, great video. Never tried but will do when I make that complicated mesh. Regarding backing in 3DS Max. Do you have any video about it? I am new to 3D programs, and didn't get to render preferences yet. I know that Vray is awesome, I saw a lot of terrific results but concentrated on learning about modificators, I'd appreciate if you can share any video tutorial  .

Mathcope for the earrings that I recently posted I created the texture 2048x4096 and also scaled RLES accordingly. I didn't try to use default size of the textures to compare but I think mine looked pretty sharp (but my pieces of texture were pretty big, I used as much space as I could to place circles). Probably I have to make 1024x2048 and compare.