OSPF is a link state routing protocol used to exchange routing information between routers within an IP network.
OSPF will not “speed up” your network in terms of throughput, latency or jitter. If by speed up your network you mean in terms of convergence then thats is likely if comparing it to other routing protocols.
If you want to configure OSPF as your routing protocol of choice then I would first of all ensure that all routers in your network supported the protocol and then perhaps did some more reading.
If you let us know the vendors of your equipment then perhaps I can give some more guidance or configuration templates.
I agree.. If you’re running an All-Cisco environment, then I see no harm is using EIGRP for your interior routing (as it is the fastest converging IGP). If you have a mixed-vendor environmet, then OSPF is a great alternative…
And, to answer you more directly, ALL of the inter-connected routers would need to have the sasme routing protocol on them (ideally) for smooth operation…