Hi Asha,
I will try to answer some of your queries to the best of my knowledge.
1. Here’s the link to 13 week study plan -
gmat-ninja-study-plan-week-400295.html - this link is for the first week of 13-weeks, and it also includes links to subsequent weeks.
2. GMAT Club does promote events based in multiple timezones and it is usually taken care that the event timings are fair for all the timezones. For example the recent MBA Spotlight Fair, where the top MBA colleges from around the world gave their presentations, started at 9:00 am US time and most of us in India attended it midnight

Also, events such as Christmas competition where questions are posted each day, the timings are morning US and evening India.
3. There are multiple
error log templates, sharing some links here
new-error-log-with-timer-for-gmat-practice-244687.html ,
gmat-error-log-86232.html , you can choose one that suits you best. I personally download my in-built GMAT Club
error log, and if I want to add some question I add it there in the column that has question links.
4. Apart from things you mentioned, GMAT Club offers
Forum Quiz, multiple other Study Plans - apart from the 13 week one, reviews of admission consultants and gmat prep companies, admission decision trackers, "what are my chances tool" to check based on your profile what schools can be considered, deals on gmat prep from third parties, admission consulting and more,
Interview debriefs, and more. I might have missed some things but GMAT Club offers mostly anything and everything related to your GMAT and Bschool prep.