Actually, certain baby pokémon do better when placed in groups, rather than separated, even if that group consists of various species. This is especially true with pokémon either known for bringing happiness (happiny) or that evolve via levels of happiness (igglybuff and togepi). This is because socialization helps them develop a healthy mental state and allows them to form the bonds that eventually lead to the development of their abilities or to their evolution, respectively. Likewise, none of those pokémon are particularly discerning when it comes to their companionship (or at least, not generally speaking), so quarrels between any of them are unlikely.
So to answer your first question, absolutely, those three will make excellent playmates.
To answer your second question, believe it or not, the same sorts of toys you would give a human baby often work well for these pokémon. Soft toys, durable plastic toys, and anything that lights up and makes music are all excellent choices—especially the latter if you’d like something that will ensure they’ll stay in one place when you take your eyes off them for a moment. Never give them anything that can fit in their mouths and be swallowed, especially igglybuff (as it will attempt to chew anything). It’s also a good idea to give your happiny a round, smooth stone the shape of a chansey egg (but slightly smaller, so she can carry it), as happiny take comfort from carrying one of these around. Yes, it’s a good idea even if you don’t wish to evolve your happiny right away. Don’t worry—the round stone isn’t happiny’s only evolutionary requirement. Also, keep a stock of these stones on hand, and make sure they’re as close to identical as you can get them. Your happiny may lose her stone often, and it’s worth it to have a replacement ready.
Best of luck, anonymous, and congratulations on the new litter!