I built a couple extensions to my house like an alchemy lab and bedrooms but when I access the drafting table again, it just has the remove benches options. I can't add alchemy stuff to my house or a plant room. Actually, I can't build anything else, the entire house if pretty bare even after telling lydia to furnish the place up

The workbench outside the house is to build the wings and exterior amenities; you use the workbenches inside the house to furnish it. Each wing has a workbench, plus there are three (if I remember correctly) in the Main Hall, and one in the cellar. Once you finish furnishing an area, you can use the workbench outside to remove the workbench in that area; this is advisable in order to avoid crashes.

How come I checked the inside benches and I can't build alchemy labs plus I checked the outside bench and I can't build anymore extensions like weapon room

Extensions to the houses are limited by the side of the house you build them on. You can only have one addition to each side, and you can only build the extensions on the outside workbenches. And once you've built them, you can't change them for something else unless you reload a previous save.

East Wing - you can build the Kitchen, or the Library, or the Armory.
West Wing - you can build the Bedrooms, or the Greenhouse, or the Enchanting Tower.
North Wing - you can build the Storage Room, or the Trophy Room, or the Alchemy Tower.

An alchemy lab can be built in the Main Hall--check the downstairs workbench for that, under "Misc". If you've built the Alchemy Wing, it should also be an option on that workbench, again, under "Misc". Really not necessary to build two, though.

But I just noticed that you said you asked Lydia to furnish the place, so it's best not to bother trying to build stuff yourself. She'll furnish everything (and I mean everything) in the rooms, but it'll take her awhile.

I guess I'll abandon this house since I screwed up

it's always a good idea to save frequently when building your house, at the very least before you build each extension. That way if you change your mind you can easily try something else.

Well this svcks big time...what a waste