How long (approx) did it take you to get to 1k?
About six months. There was several reasons for this long period. No idea of LaTeX, nor SE rules (written and no written), my poor English not used to deal with programing & typography jargons, no pressure to gain reputations, pressure of my dogs that need walk daily, etc.
I did not seem difficult to win 1K but impossible, because in the rare case of know a good solution, there is someone faster and more expert able to reply in few minutes as soon as you look away while you are wasting 20 minutes making a good example and some explanation. So most of y solutions ended in the trash.
If you were to create a new user and start over, how long do you think it would take for you to gain 1k rep?
Not sure, but munch less. With now years of writing only with LaTeX and procrastinating in SE everyday, who not will learn something about LaTeX, make effective answers and the written and not written "netiquette" in SE?
Do you accept this challenge?
No. Among few things that I learned (not only here) one is not to tempted excessively by challenges where the reward are fake points.
Are you mostly gaining rep from old questions or new ones?
Old question. My most frequent silver badge is Necromancer ... I know. Is the terrible strategy to gain reputation. Who hits first hits twice. Recent question have highest attention to possible solutions and there are not still answers from competitors, so you have munch more chances of be accepted and upvoted.
But I focused more in older questions, even with several accepted answers and one accepted, out of the top list, because probably I could work quietly in provide alternative solutions, without the risk of post too late. The problem is that will receive visits occasionally, and then people will see your non accepted answer of 0 upvotes beside others with maybe several dozens of votes, so the first feeling is that your solution is probably wrong. But I do not care, my motivation was never reach the top users of TeX.SE
Do you have a life?
You mean other life that read dozens of useless messages in your email account, dozen of silly dialogs in Whatsapp distracting you of talk with person in front of you, consume trash TV, see yet another zombie movie, listen the lies of politicians, fill every day several forms that stupids bureaucrat have devised ?