Baggage claim during changing flights

In order to check in, do I have to claim my baggage first then find the operating airlines to check in, or, is it something like notifying them that I am there to claim my seat?

You should find out when you check in for your first leg. Usually you will be checked in for any unconfirmed legs at that point, though you may get a boarding pass that still shows an unconfirmed seat. This has happened to me a few times in the past.

The bag will normally be checked to the final destination, and you'll normally get a seat assignment at the gate or at transfer desk in the airport from which the unconfirmed leg departs. It's possible, however, that your bag will be checked only to that airport, in which case you may have to retrieve it. The agent who checks you in at your point of origin should clarify exactly what you need to do.

Do I need transit visa, layover is around hours, to change terminal (3 to 5) at Manchester. MAN to ORD is operated by American Airlines.

Whether you need a visa for the UK, and if so what type of visa you need, depends on your nationality (which you have not disclosed) and on certain other facts. You can learn about the requirements elsewhere on this site at Is there a way to find out if I need a transit visa for a layover in the UK?

If you need to retrieve your bags, you will need to go through passport control. Note that most people who would normally require a visa may be able to qualify for the "transit without visa" concession if (among other conditions) they have a visa for the US. Another condition that must be met is that your departure must be either on the same day as your arrival or before midnight on the following day.

Baggage you can check with your airline on your first leg.

For the visa I got this from the UK governments website. This is if you are an Indian citizen which I am presuming. If you are not check that link and fill it out. I have bolded the points which apply to you.

You’ll need a visa to pass through the UK in transit (unless you’re exempt) You should apply for a Direct Airside Transit visa if you arrive in the UK on a flight and leave again without passing through immigration control.

Exemptions You don’t need a visa if you have one of the following:

• a visa for Canada, New Zealand, Australia or the USA (this can be used for travel to any country)
• a residence permit issued by Australia or New Zealand
• a common format residence permit issued by an European Economic Area (EEA) country or Switzerland
• a resident permit issued by Canada after 28 June 2002
• a uniform format category D visa for entry into a country in the European Economic Area (EEA) or Switzerland
• an Irish biometric visa (marked ‘BC’ or ‘BC BIVS’ in the ‘Remarks’ section)
• a Schengen Approved Destination Scheme (ADS) group tourism visa where the holder is travelling to the Schengen country that issued the visa
• a flight ticket from the Schengen area, if you can prove that you entered the Schengen area in the previous 30 days on the basis of a
  valid Schengen ADS visa
• a valid USA I-551 Temporary Immigrant visa issued by the USA (a wet-ink stamp version will not be accepted)
• a valid USA permanent residence card issued by the USA on or after 21 April 1998
• an expired USA I-551 Permanent Residence card issued by the USA on or after 21 April 1998, with a valid I-797 letter authorising extension
• a valid standalone US Immigration Form 155A/155B issued by the USA (attached to a sealed brown envelope)
• All visas and residence permits must be valid.

So if you have a valid US visa that applies to one of these you can transit without a transit visa.