Here's some answers to your questions:
1) Gardening is not a skill. It's a Talent Badge. This means you are going to have to grow tomatoes, apples ect. and because there is no garden in your sim's apartment, she can't work on this talent badge.
2) Sims living in apartment cannot join in the Gardening Club. That is correct. Seasons expansion pack came before Apartment Life expansion.
3) No, sims can't learn skills and talent badges on the community lot. However, if you own the Open for Business expansion pack, try buying a community lot. Then you can have your sim get that Gardening talent badge there.
4) Garden club does not give invitations to sims. You may see garden club townies roaming around, but they only sell the potion that cures plantsims. +You can't call the gardening club in there by phone to review the "garden" too...
Tips on getting on that secret lot:
1) Forget the Gardening club! They are not important here. As they came in the Seasons and hobbies and these secret lots in FreeTime expansion pack, there is no connection between them. Gardening club does give wishing wells to sims who have the parfect garden, but wishing well can lead to death if your sim wishes for money too much...
2) Try other activities beside of gardening. Have your sim collect bugs, watching birds, studying cleaning, watch clouds and talk about that hobby. If your sim's Nature hobby enthusiasm reaches level 3, you'll get a phone call asking if you want to subscribe to the magazine. Choose yes, because it is a great way of building the enthusiasm.
Remember, your sim's hobby enthusiasm must be on level 5 in order to get access to these secret lots, so keep doing these activities. Also be on a lookout at the chance cards when your sim is working, because it can give you access early.
I'd recommend that you check out this The Sims Wiki page (sims.wikia.com/wiki/Nature). It lists all the activities in order to raise sim's Nature hobby enthusiasm.Good luck and happy simming!
