I want to transfer coins to multiple exchanges, how can I do it?
Just open accounts on all those exchanges and then get deposit addresses. Transfer funds howefver you like.
Can I split coins from one wallet into the exchanges?
Do I need a specific kind of wallet?
You can just withdraw from wherever your coins are now to your deposit addresses at various exchanges.
And when I withdraw coins from an exchange, can I withdraw only a part of my funds(and leave the rest in my exchange account)?
As far as I know, every legitimate exchange supports withdrawals of whatever amounts you want. Typically there are minimum withdrawal amounts and some withdrawal fee to cover the transaction cost, but that's about it.