I have recently bought Breezehome and since I have Dawnguard installed it never gives me the alchemy lab. Can I uninstall Dawnguard then get it back for free since I have already purchased it. Or after removing it will I not be able to load the save?

If you load a previous save you should be ok, but Bethesda has not fixed it yet. It does not affect characters who have all ready purchased the home though.

Already done, I reloaded a save from before I got the option to buy the house but it still glitches. If I uninstall it will I lost my items on a different save that has completed Dawnguard. Or does that happen when you reload.

I think that only happens if you reload that different save without Dawnguard being installed. Sadly, I can't confirm that for you.