Dhcp same subnet different vlans

1. I wouldn't restrict yourself to just that .1-.30 range for servers, it might seem like a lot now but those IPs can run out very quickly indeed, there's also no need whatsoever for them to be in the same class-c as their clients. So give your servers lots of room, say 192.168.1.0/24 and don't start your clients until say 192.168.8.0/24, there's no downside to doing that. That said you should really carve up your subnets either by L3 switch/switch-segment or by building/floor etc. It makes no sense to just have them all in one VLAN - it may seem easier but it'll make management harder further down the line, and don't scrimp on IPs per segment either, there's no hard rule on giving each a /24 - your router won't care.
2. It's not advised to put your servers in the same subnet as your clients unless you have a really valid reason such as massive client-to-server traffic or have seriously overloaded routers. By putting them in the same subnet you lose some degree of control that you may wish to have later.
3. This is kind of the same question as above, yes, keep them separate, it's the 'Layer 3' bit of the switch that does the work here, essentially it means the switch can route between subnets, often very quickly indeed and with hardly any latency - but doing this give you a lot of control and support options that you may benefit from further down the line.

If these two VLANs are separate and there will be some form of NAT-ing happening between them, then yes, this is certainly feasible. Though in my own corporate network I would try to eliminate possible confusion (human or technological) and just give them all their own IP ranges.