Ich mache heute einen kurzen Beitrag, dasin dem es um das Verb "sich über/auf etw. freuen" gehen wird.

It's always either 'es geht in x um y' or 'x handelt von y'.
The relative pronoun refers to 'Beitrag', therefore it has to be masculine singular and according to its function in the relative clause it has to be dative.
When talking about a verb, you usually explicitly state all the objects it can take.

Ich höre und lese dieses Verb ständig, vor allem beim Podcasts.

'Podcasts' should definitely be indefinite plural, therefore no article in 'bei'.

Ich mache/gebe ein paar Bespiele dazu:

If you say you 'mache' the examples, you stress that it was you who came up with and created these exact examples, when all you probably want to convey is that you're showing some examples.

Ich freue mich auf das schönes Wetter morgen.

Adjectives decline differently after definite articles. Whole lot of learning.

(I am looking forward tover the nice weather tomorrow).

Yes, seems a bit petty to correct the English as well, but the English verb is 'to look forward *to* sth.'

Ich freue mich über das schönes Wetter heute.

Same as above, declension after definite articles.