I have learnt two points about "to-infinitive" as follows.

verb + to + infinitive

Its meaning is similar to "in order to" or "so as to".

• I come to pick you up.
• She runs to catch the bus.

adjective + to + infinitive

• It is hard to learn many languages simultaneously.
• This book is difficult to comprehend.

Question

Does the structure "noun+to+infinitive" exist in English grammar? For example:

• I lend a screwdriver to open your watch.
• I am the math teacher to substitute for Mr. X who is absent today.

Bonus question:
What is the difference (if any) between the following sentences?

A: This book is difficult to comprehend.
B: This book is difficult to be comprehended.

Yes, that pattern with a noun is grammatical.

What's this?
-- It's a hat to put your beer in when you go to the football game.

Here's a screwdriver to open your watch with.

The construction indicates "intended purpose".

Your teacher example is not right if your desired meaning is "I am the substitute". Normally there'd be a participle clause there for that meaning, ...teacher substituting for ....

There's a prospective sense in this noun + infinitive construction:

We're going to make a presentation to Acme Widgets next week.
-- Joe's the man to take with you. He knows their product line very well.

Joe is suitable for the intended purpose, namely, making a presentation to Acme Widgets.

So your sentence about the substitute teacher would be valid in a discussion about who would be a suitable substitute teacher for Mr. X; you would be suggesting that you are a person suited to that job:

I don't know who we should send as the substitute teacher.
-- I'm just the math teacher to substitute for Mr. X, since I taught those students for most of last semester while Ms. J was out on maternity leave.