This is the case by default. Users start at trust level 0 with posting, replying and creating topics available to trust level 0.
You can search the settings at the top of that page, searching for “personal message” will give you what you want for this. Specifically, the setting is enable personal messages.
I don’t think you can disable trust levels entirely. However, tl4 is only available manually and tl3 can be disabled by setting the tl3 requires days visited to “101”, 1 higher than tl3 time period.
What you can also do is disable send tl1 welcome message and send tl2 promotion message, as well as adjust the other settings inside Trust Levels such that tl1 and tl2 do not confer any benefits over tl0. The ones to care about are all at the top of the Trust Levels section, besides two right at the very bottom.
In Badges, you can also find and disable the Basic and Member badges which would be awarded at tl1 and tl2. These changes should make tl0-tl2 largely invisible and have no effect on what users can do.
Search the settings for “approve” and you’ll find two unless trust level settings. Set both to tl3 or tl4 (depending on whether or not you want to allow manual tl3 users to be able to post without approval) and you will need to approve all posts from users you haven’t manually trusted.
Disabling edits can be done by setting min trust to edit post to tl4.
The theme selector in the menu comes from a theme component, which can be installed and added to all themes.
This can be controlled by the order of the top menu setting, that is whichever item you put first in that setting will be the default. I use categories, latest, new, unread, top myself, where new and unread get hidden if there aren’t any.
In general, most of the settings are fairly easily searchable when you find a behaviour you want to change, just be careful of inflection. For example, if you wanted to change a behaviour related to deletion, search for “delet” because some settings might use “delete” while others use “deleting”, etc.