Part 135 Scheduled Operations vs 91
 

I recently passed my 135 initial ride working for a 135 single plane single engine and single pilot operator flying a Cherokee. So my company was waiting for me to pass the checkride for a long time due to weather and FAA under staff, and they have already had a contract lined up.

Prior my checkride, I was asked take their contract client from point A to point B in the morning and return in the afternoon under 91. They said the client(Company A) is leasing one of our flight school aircraft which owned by a leasing company (Company B) and a pilot (Me) from flight school (Company C) so the flight is totally legal fly under 91 even its technically a Part 135 operation as company B and C owned by the same person and my pay comes from company B. I of course turned down the flight at the end because I did not believe it legal to do so. Does anyone have different interpretation for this scenario?

Shortly after I passed my checkride, my company just can't wait to make all these big money, so they asked me to do a regular flight for the Company A from point A to point B in the morning and return in the afternoon same time Monday through Friday, and in this scenario my duty time supposed to end by 6:00 pm. I told them I need to have 10 consecutive hours so I won't be able to take any assignment after that time, but they said I can have bed at the airport or rest in the crew lounge at the FBO for few hours so it will reset my rest period....as far as I know I am not allow to conduct scheduled flight under 135, in this case if the client wants us to conduct flights Monday through Friday same locations, same time, does that fits into "Scheduled Flight" category?

Not close enough to a reference right now but my answer is no.
There is a provision for scheduled 135 but I've always understood it to be the company that sets the schedule rather then the client.
I would venture to say you're ok but keep an eye on those duty times.
The FAA is very aware and very eager to bail you to the wall over duty times.
It's considered careless and reckless operations also, because of fatigue issues.

Your first scenario could very well be legal under Part 91, depending on the lease arrangements.
Having a 135 client that wants to go on a trip at the same time on multiple days does not constitute a "scheduled" operation by FAA definition. As B2N2 mentioned, that is more like an airline schedule, where the 135 company has a "Flight 1273" departing 0730 every day, or such. Duty times, I can't tell from your description exactly what the situation is, but yes, in general, a rest period must be 10 consecutive hours, and that means free from any duty requirements, not on call, not required to answer a pager or company phone call, etc. There is no required standard for rest location, so theoretically, the company could leave you in the crew lounge, or on a cot in the back of the hangar, or even with a sleeping bag on the floor of the plane, as long as it meets the 10 hours. A good company, though, would provide a day-room at a hotel or a crew apartment for the rest period. So, for a client that wanted a long day away, let's say you start the day at 0700, and arrive at destination and are off duty at 0900. To stay within one duty day, you would have to be "back home" and done flying by 2100. However, if you stay there, completely off duty, for 10 hours (or more) your new duty day could start at 1900, to take the client home, but not before, with the new duty day going up to 14 hours, or all the way till 0900 the following morning.
Many of the small freight feeders (FedEx caravan or UPS contractors) run on a schedule like this, the pilot rest period is accomplished all day at the "out-station," rather than at night where the flight originates.
That scenario must also be arranged prior to going off duty. It does not meet the legal standard for rest to be pacing around the FBO crew lounge all day thinking the client may show up for departure after, say, 8 hours on the ground, but they stay longer, and show up, for example, after 11 hours.

Make sure who has "operational control" over the plane. This can easily be illegal, read the AC on these ops.

Easy way of understanding "operational control":

Customer tells your employer where they want to go.
Employer contacts you and tells you (dispatches) where to go.
Customer cannot show up and arbitrarily change the destination.
They need to call your employer and you need top be re-dispatched.

There's a little more detail to that but its the big picture.

The most common trap people fall into is, that customer A rents a plane from place B, then tells pilot C he wants to go here.
Pilot C then does all the scheduling, dispatching and planning of the flight. This is not allowed, and it's on the pilots ticket too because he has operational control over that flight then.

When the pax (read lessor) decides who will be the pilot, and where & when the flight will go - they have operational control. If any other body has control over any one of these then the pax does not have ops. control and the flight would not be considered a legitimate lease, operating under Pt 91. Now you enter the dubious world of '134 1/2'. Be prepared for a profoundly unpleasant time if the FAA catches you.

Part 91 doesn't have flight & duty time limits, apart from careless & reckless ops. If the op is part 135 (as most 135s operate) then *all* rest must be proscriptive. *No* rest can be retroactive. Doesn't matter if it was daily, weekly, monthly, or quarterly. If you can't plan to have a beer, then it does not count as rest. No amount of 'well, we didn't call you so therefore it's the same as rest', or 'we won't call you but be ready to answer the phone' passes muster. There are numerous - and consistent - FAA legal interpretations of this going back 20 years or more. It is not open to interpretation.

Something else to consider: Under Pt 135 many have maintained 'legal to start = legal to finish'. Not quite so. WRT to *flight time* that can be the case. The regs. specify extensions to flight time limits, and the rest penalties as a result. BUT! They do NOT specify any normal way to extend duty time ie unless it's an emergency - which allows you to break any rule to deal with that event for a safe outcome - you cannot extend *duty time*.