In college, my Japanese teacher told us that a lot of foreigners get these characters wrong, but if you know the stroke order then it's easy to see the difference.

シ (shi) is written top to bottom. You can see that all the starting points for the strokes line up vertically on the left. Also, the last stroke curves from the bottom-left to the upper-right.

ツ (tsu) is written from left to right. You can see that all the starting points for the strokes line up horizontally at the top. Also, the last stroke curves from the upper-right down to the bottom-left.

ン (n) lke 'shi' is written top to bottom. The starting points for the strokes line up vertically on the left. It also uses the same direction for the longer, final stroke as 'shi'.

ソ (so) like 'tsu' is written left to right. The starting points for the strokes line up vertically on the left. It also uses the same direction for the longer, final stroke as 'tsu'.

All the kana are easy to learn if you use mnemonics, though I admit handwriting recognition might be harder. It took me a moment to recall some of the mnemonics themselves, eventually you just see them as they are... For tsu, I can think of Two sewing needles, for shi, I can think of "she has a funny face", for so it's one "so-ing" needle, for n it's a cyclops who can only say "nnnnnn". (https://www.tofugu.com/japanese/learn-katakana/ and https://www.tofugu.com/japanese/learn-hiragana/ have some great mnemonics to start out, I remember only altering a few.)

On their own they don't mean anything, however the first four may appear and indeed do as multiple words on their own, or as part of other words. Japanese has many homophones.

Actually Katakana derived from Kanji, but were typically only used for their sound rather than their meaning and a very very simplified version of how you would write the character quickly allowing for lifting the brush (Hiragana is the simplified version quickly without lifting the brush) roughly speaking; so you are mostly right but not completely.

シ comes from the Chinese character 之, meaning either "of" or "this"

ツ comes from the Chinese character 州 (although some researchers disagree), meaning "state" or "province"

ソ comes from the Chinese character 會, meaning "meet", "party", or "interview"

ン comes from the Chinese character 尓 (again not clear), meaning "you" or "that"

This divergence happened because Chinese characters were used to write Japanese which is mostly from a different language family. Some Chinese characters were used by some for their meaning (ideogram) and used by others for the sound they made to approximate the sounds used in Japanese. Obviously Chinese influenced the Japanese language (for example numbers in Japanese sound similar to numbers in middle ages colloquial Hokkien). Over the last 1,000 years or so there have been numerous occasions for changes, standardisation and simplification. So even to those who study these changes over time it can sometimes be unclear.