I would suggest trying out the translate function. For example, for the first requirement, you could do this:
translate(field1, " ", "")
where spaces are "translated" into nothing. (removed)
You could use another translate function to translate all uppercase letters into lowercase, to end up with something like:
translate(translate(field1, " ", ""),"ABCDEFGHIJKLMNOPQRSTUVWXYZ","abcdefghijklmnopqrstuvwxyz")
I'm attaching a quick sample. Hope this helps.