Q: Can I increase storage and speed to my iMac computer?

Welcome to the Apple Support Communities

Apple won't replace the hard disk because it will avoid warranty, but you can do it yourself if you prefer

If you have a large photo Library consider moving it to an external hard drive. The OS requires a minimum of 10 to 15 GB of space at all times, more is better.A nearly  full hard drive can cause speed issues, so can lack of enough RAM. An AASP will  put a new hard drive in your iMac, doing it yourself is not for the faint of heart.

T ~ Welcome to the Support Communities. If you want to use an external hard drive for your iPhoto library, this Apple doc may help:

iPhoto '11: Move your iPhoto library to a new location

And regarding improving your iMac's speed by increasing its RAM:

iMac: Memory specifications and upgrades

...Found by searching HERE.