I urgently need to know if the following sentences are all possible. Thank you.

1)I didn't know your address but I manged to/was able to/ (but not could) find you.
2) When I was young, I was able/could play the guitar quite well.
3) I called Mary many times yesterday evening, but I wasn't able/couldn't/speak with her. (also: didn't succeed in speaking with her):
4) Would you like to have lunch with me?
5) He invited me to have lunch with him. (NOT: He proposed to have lunch with him/ He proposed having lunch..)
Does the word "writing material" exist?

1. managed

2. OK

3. last evening

4. OK

5. OK

The term "writing materials" (note the plural form) exists and refers to having pen/pencil and paper at hand.

those sentences seem great to me. With num 3 use (able). Try also to make your sentences as interesting as possible.

To determine if the given sentences are all possible, we can analyze each sentence individually:

1) "I didn't know your address but I managed to/was able to/find you."
This sentence is grammatically correct and all three options ("managed to," "was able to," and "could") are acceptable, with slightly different implications. "Managed to" often implies overcoming a difficulty or challenge, while "was able to" simply denotes capability. "Could" in this context may be less common but can also be understood as having the ability to find the person.

2) "When I was young, I was able to/could play the guitar quite well."
Both "was able to" and "could" are correct and convey the same meaning in this context. They both indicate past ability.

3) "I called Mary many times yesterday evening, but I wasn't able to/couldn't speak with her (also didn't succeed in speaking with her)."
Again, both "wasn't able to" and "couldn't" are correct and convey the same meaning, indicating the inability to speak with Mary. The additional phrase "didn't succeed in" is also a valid alternative to express the same idea.

4) "Would you like to have lunch with me?"
This sentence is grammatically correct and is a polite way to extend an invitation for a lunch gathering.

5) "He invited me to have lunch with him (NOT: He proposed to have lunch with him/ He proposed having lunch)."
The given sentence is grammatically correct. "Invited" is the appropriate word to use in this context, whereas "proposed" may imply a formal suggestion or idea rather than a casual invitation.

Regarding the final question, "Does the word 'writing material' exist?"
Yes, the term "writing material" does exist. It refers to the objects or substances used for writing, such as pens, pencils, papers, notebooks, etc.