The word "כלום" is more like "nothing" rather than "anything". Not sure I can explain exactly why, but "אני לא רואה כלום כזה" just doesn't work. You could say "אין פה כלום" but ״כלום״ can't be "like this". You wouldn't say "I can't see nothing like this" in proper English either.

No. דבר is male so you would always use ״כזה״.

כזה.

When you say "כזה" it means, "like this" or "like that", as in this sentence, with a specific object or situation in mind.

את רואה שולחן אדום?

אני לא רואה שום דבר כזה.

Whereas "ככה", even though it would still be literally translated as "like this", is more of a general descriptor of a way that things are:

למה אתם עושים את זה ככה?

כי ככה יותר נוח לנו.

... Or even used as an empty explanation (imagine this spoken by impatient parents to their young children):

למה?

ככה.

(See: https://www.youtube.com/watch?v=N_2Ivfm5xME )

or even...

אז מה?

אז ככה!

(See https://www.youtube.com/watch?v=yPjZLlcnnDg )

It might help to think of "ככה" more as "this way" than "like this". It's a bit context dependent.

I'm learning too, I can tell you I saw ככה used on crafts videos on YouTube. like, here's how you do this stitch: (like so) Kakha... (I accidentally put it on, but the kid had such a great voice for learning I kept watching... and watched others! ) how to make a bracelet from rubber bands (smh.... ) ככה... https://youtu.be/x1cvesMOm8A

According to the dictionary on morfix.co.il "משהו" means "something" and "שום דבר" means "nothing"

Yes, that's the correct pronunciation, and Hippopigamus is correct about the difference between the two.

Like this: https://music.youtube.com/watch?v=UbENMrCQgRo&feature=share

Song is: משהו מתוק, פבלו רוזנברג ופאר טסי Something Sweet (Pablo Rosenberg & Pe'er Tasi)

Yes, you could use it, and yes, it would be antiquated, and it would be spelled "אינני" rather than "אנני".