Old Habits - Adverbs of Frequency

Answer 2 is the most characterful and accurate way of putting this.

Answer 2 has the strongest turns of phrase. Answer 1 is simple and workable; Answer 3 is understandable, but not what we would say. Answer 4 is quite good; 'turned up' is informal, with a slight sense about it that the uncle wasn't expected. If 'he' really was your uncle, we might assume that his sister is 'your' mother, and she would not be 100% happy about a grown-up coming along most weeks to assume he can use her washing-machine (especially if 'you' were part of a growing family of children at that time).
Your own language may also be good at suggesting context, through use of adverbs and other choices of phrase. If you can build this level of detail into your storytelling in English, even sometimes, that would be splendid.

Any of these starts (up to the comma) would make good idiomatic sense, but only Answer 1 has the second part that fits on properly. You can't 'succeed to do' something in English (Answer 4), though there is another rather similar-sounding usage with an unrelated meaning.

Answers 1 & 3 are also quite good, and acceptable language-wise, but No.2 carries the best nuances and turns-of-phrase: 'back in the 60s' subtly but clearly emphasises the time-gap of half a century or so (a very long time indeed in terms of a new field like computer technology), while 'was already building' suggests that he had what we'd call 'a head start' on his competitors, in terms of gaining direct experience and knowing more than they did. This is much the strongest, richest Answer.

' ... Read us ... ' is simple and standard English; we do not need to use both the 'would' and 'use[d] to' to establish a routine or habit in the past.

In English you are more likely to 'go and stay', rather than 'go to stay ...', though some people do use this form.
It will be 'at my grandparents' ' (note the apostrophe: this means 'at the house belonging to them'. That is why the option with 'with' (Answer 3) would not quite work accurately.

Answer 1 is somewhat 'bald' and factual; Answer 2 is the mellowest, with a suggestion that the disasters were fairly frequent but perhaps not always as serious as they 'seemed'. Answer 3 is possible but very literary and old-fashioned; Answer 4 is the only really weak option this time.

Answer 1 is the best, though there are good elements in each of the others.
The machinery may have cost the farmers a lot to install, but could be run by far fewer staff, bringing a saving on wages. The Industrial Revolution was already well under-way in Britain two centuries ago; it was in Britain that it first began.

Answer 1 is fine, if simple: more suited to the early stages of a biography when 'she' became famous later in her life. The later versions here each catch rather more of the sense of surprise and unusual achievement.
Answer 3 doesn't quite work, because 'she' only has one 15th birthday, and it doesn't make clear sense for her to be doing five nights'-worth of dancing within 24 hours ~ however good, keen, talented, pretty etc. she may already have been.
Answer 4 is fine if unremarkable; it does not carry the same strength of nuance as No.2.

'Often' emphasises that this was frequent ('usually' suggests almost every day, which may not be so likely); we 'go for' a walk, in English, rather than 'doing' it as in some other languages.