The difference is very simple

"Although" must be followed by a clause (sub.+verb) like "she was tired" & it can also be followed by a past participle or an adjective like "tired"
So, you can say "Although she was tired,.............." OR "Although tired,............"


"Despite & Inspite of" have the same meaning & usage.
They are both followed by a noun or a gerund (verb+ing)
So, you say "Despite feeling tired,.............."
"Inspite of having alot of money,..............."
"Inspite of the bad weather,he went out"

[I wish you have got the clue]