Fix and Update Basic Usage's and Core page

[vairodp]

Description

Fix the Basic Usage page docs, by updating the code, fixing it, and also fixing the grammar.
In the second commit I fixed also the API -> Core page, by removing deprecated docs, fixing grammar and inconsistencies

Type of change

Please delete options that are not relevant.

• Bug fix (non-breaking change which fixes an issue)

Checklist:

• I have run the pre-commit checks with pre-commit run --all-files (see CONTRIBUTING.md instructions to set it up)
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• My changes generate no new warnings
• I have added tests that prove my fix is effective or that my feature works
• New and existing unit tests pass locally with my changes

[pseudo-rnd-thoughts]

Amazing, I will read through all of the changes tomorrow evening.
Are you going to review any more files for this PR?

[vairodp]

Amazing, I will read through all of the changes tomorrow evening. Are you going to review any more files for this PR?

Not in this PR, my plan is to do a PR for every "section" of work that I'm doing and I've already done another PR for the tutorial section.
If you think is a bad idea I can continue my work in this PR

[pseudo-rnd-thoughts]

This looks good except for the gymn to gym