I rememberMoscow when I was 5 years old. * visit
to visit
visiting
2. My sister doesn't let meher smartphone. *
take
to take
taking
3. I would preferyour umbrella, if you don't mind. It's raining cats and dogs. *
take
to take
taking
4. He triedhis eyes open, but he fell asleep at 9 pm. *
keep
to keep
keeping
5.If Helen doesn't answer, tryher sister. *
call
to call
calling
6. Remembersome vegetables and fruits for supper! *
buy
to buy
buying
7. Don't you mindthe window? It's too hot. *
open
to open
openning
8. May Iyou some questions, Mr. Brown? *
ask
to ask
asking
9.I wantto italian pizza festival this summer. *
visit
to visit
visiting
10. She's clever enoughthis Maths test. *
take
to take
taking

1) they were norsemen of scandinavia who in their ships braved arctic seas to make their way to greenland in 985 ad.

to make -- an adverbial modifier of purpose обстоятельство цели

2) their method of reading was to read one line from left to right, then to come back and to read the next from right to left.

to read, to come back, to read – part of a predicate (predicative) именная часть сказуемого

3) to preserve the traditions under these circumstances was very difficult and they were not preserved.

to preserve -- subject подлежащее

4) the right to organize a guild was granted to the first towns by the owner of the land who might be the king, abbot or some other powerful lord.

to organize -- attribute определение

be – part of a compound verbal modal predicate часть составного глагольного модального сказуемого