My thoughts:
1) How long can I take to write the GMAT again??
Generally most program review on a rolling basis but will typically lump you in with the subsequent rounds of evaluation, so you want to try and get the GMAT done sometime during the evaluation period which is usually starting at the deadline and a few months after that for each round
2) Will they wait for my score or update on my profile for 6 weeks if I send them an update after 3 weeks saying I have progressed in my job and ask them to hold on??
They will not wait for an update from you, they will evaluate the information as it comes in but a decision will not be automatically come just because you provide an update. But depending on the timing of the decision you may be able to get both updates in. Part of your initial update can reference a forthcoming update on your GMAT
3) Would a new job offer strengthen my profile now ??
If the job offer, is an upgrade or an improve in your profile that aligns with your future career and development goals, it can be seen as a positive