(1) How do you pick up items without having to equip them?

(2) It seems that only a few types of Mages and Fighters guild advances the player. I am currently located in Pothago, which is west of Sentinel and the only Fighter's guild I found that can advance the ranks of my PC is located at Daggerfall: Daggerfall. Is there any one that's closer or is it something I have to check because towns are randomized? For the record, even the province of Sentinel itself doesn't seem to have any Fighter's Guild that advances my PC.

highlight the remove command to take an item instead of the equip command

You should be able to rank up anywhere, at least for the first few ranks. You rank up when you have enough reputation with the faction (from doing quests) and have your skills to a high enough level. Personality score may also have something to do with it

2.) Any fighters/mages guild can rank you up. If you've done a ton of quests and nothing happens, it may have to do with your skills, there are minimum skill requirements for certain ranks in all guilds. In addition, you can only level up in the guild once a month, so if you've recently leveled up in the guild you have to wait.

That's weird... I definitely have the skills.

From my observations, I can level up in Mage's Guilds and Fighter's Guilds that have a different layout than the one I regularly go to. So I assume all Guilds of the same tier are considered the same?

Anyhow, I am not sure if a month has been passed since my last promotion. However, it's been quite a long time since I got one although I don't do any travels that take more than 1 day.