PPI its been 8 weeks should I go to the ombudsman?

Should I be escalating the claims to the ombudsman after the 8 weeks?

No. It is well documented that there was a last minute surge and not many are getting resolved within 8 weeks.

Is there any advantages or disadvantages in waiting longer before escalating to the ombudsman?

No advantage as the FOS is behind as well and you just enter a new queue. Further disadvantages are that a firm may well auto-payout if you havent referred it to the FOS but are less likely to if you have as they may as well wait for a FOS decision.

Be patient.

However, I would check the ones you haven't had the response letter on. Resolver has a habit of not always notifying the providers and the ones you haven't heard on may never have received your complaint.

All firms are required to acknowledge the complaint and explain the process upon receipt of a complaint. You normally get it in writing within days.

Is there any maximum length of time you should wait

Not really. At the peak if PPI complaining, people often had to wait a year or two. Then another year or so if they went to the FOS. Today, you are probably only talking months.