Hi iaf_22.
1. JAR rules say something like "additional requirements as required by the Authority". The UK CAA impose no extra conditions until five years after expiry. Check what your local authority requires.
2. A B737 type rating has nothing whatsoever to do with a single-pilot IR and a multi-engine piston (MEP) rating. A completed type rating will give you a new entry in your licence ratings page which combines the B737 rating itself and a type specific multi-pilot IR (completely separate from your single-pilot IR). This multi-pilot IR is an integral part of the type rating. You'll still have to renew your MEP and single-pilot IR if you want to fly light piston twins under IFR. To don't need a valid MEP to start a type rating, only a valid multi-engine IR.
3. The IR can be renewed in an approved sim, the MEP has to renewed in the aircraft. Sim is cheaper of course, but if you want to renew your MEP separately you'll end up paying two test fees.
4. The type rating is valid for 12 months. The twice yearly check you refer to is an Operator Proficiency Check (or base check) which your company will organise once you're actually working.
Seems to me you could do with some bedtime reading of JAR-OPS and JAR-FCL
