[susan53]

No. Severely doesn't fit either of these contexts.It can be used as an adverb of manner :
He spoke to her severely.

but here you are using it as an intensifier for an entire clause - and if you look at a concordancer you'll see that it is used mainly to intensify an individual verb or adjective - eg :

This would severely limit our capacity to...
The two modes were kept severely distinct.

I would rewrite your sentences as :
1. Stress caused him to suffer from severe hair loss.
2. Their lack of experience led to a severe loss of money.

Notice that I've here changed to the adjective severe so that I can use it to premodify/intensify the noun phrase. I'm no longer trying to use the adverb as an intensifier for the whole clause. If you really want the adverb you might say :

3. Stress caused him to suffer severely from hair loss

but 3 doesn't sound as natural as 1, and I can't think of a natural sounding equivalent for the second sentence.