Questions before onboarding

1. Is it normal to still be waiting on the formal offer letter? I was given the TJO in May and have an EOD of July 15th.
2. Should I be doing anything right now? I was sent a list of action items in the TJO but other than the equipment (and the onboarding forms), I haven’t been able to do anything (fingerprints, background check, etc.). I have been told they aim to send the official email 30 days prior to the start date but I also heard they are switching hr offices or something which could be a reason for delay. Additionally, I was told I can’t really start a lot of the tasks without formal offer letter because I am not in the database for them to find me.
3. Is it common for the EOD to be pushed back? I have another offer but I set a late start date so I could back out prior to their start date, giving them adequate notice. With that being said if it’s pushed back too far I may be risking it being a big inconvenience for the other company but until an official offer arrives I can’t feel 100% certain that this will materialize.

Thank you for any assistance!