Hi Kinnari,
1. With British Citizenship, you can not only visit but also work anywhere in Europe.
2. With your ILR or PR, you cannot be out of the country (UK) for more than 2 years.
3. To visit India, you will not require visa if you get OCI (or PIO) card. OCI is better than PIO so everyone applying now will go for OCI.
A small note, after 5 years of getting OCI you can get your Indian citizenship back. So a Dual Citizenship in the true sense.
Hope that answers your questions. Feel free to ask more.
Houns