I had sent a fairly comprehensive reply but it seems to have disappeared!
Anyway here is a summary:
1. Apple will not touch an iPhone that has a third party battery fitted.
2. If you want an Apple Store to replace the battery you had better make sure that your iPhone has a genuine Apple battery, so put your old battery back in before you visit the shop.
3. The only guaranteed way to get the CPU back up to speed (1400 MHz) is to have a genuine Apple battery fitted. You might get lucky with a third party unit, but it’s not worth the risk, now that you can get it done for £25.
Hope this helps.