For the Pena Palace the pre-purchased ticket is not for a time slot.
It is just a ticket for the day and can be used anytime.
I purchased the entry ticket in advance the evening before online and was emailed PDF tickets which I screen-shotted while on wifi and then just showed the pictures in my phones camera album at the gate. They scan in with a barcode reader.
You need to show twice, once for the park entry and other for inside the palace area, assuming you are getting that combined ticket.
I just visited this Sunday ; 2 days ago
Being there before 10 AM it is not crowded. Around noon and all afternoon it becomes a zoo and really takes away from the experience.
We drove and found parking rather easy a little lower than the Moorish Castle on the road up at 10 AM, to park closer to the Palace itself I am certain you would have to get there at 9:30 in the summer.
I did also pay the 3 euro for the bus ride uphill from the main park entrance to the castle, otherwise it is a good haul uphill. Advise you do that as well and then save your legs for the walk up to High Cross after visiting the Castle, that is what we did.
After visiting the high cross and a couple of other points in the park went back to the Castle had a quick snack and the crowds were now overwhelming.
You cannot buy the bus tickets online, some people call it a tram but it is a bus.
In the morning the line was a couple of buses capacity long so expect to wait 20 min or so, and much longer later in the day.
Bus tickets you can buy in the gift shop just after the park entry which is MUCH better than waiting online to buy them at the front entry to the park.
Walked down to the road, and then downhill easy walk to Moorish Castle entry area/parking lot.
For there is a more level walk to where the castle walls are.
After the Moorish Castle we walked back down to our car and drove into town, explored the town area when into the Palacio Nacional de Sintra and enjoyed being among the crowd watching the World Cup final outdoors in the square.
Once that ended we had an early dinner and left town. Ended up not having enough time to see Quinta da Regaleira.
I wanted to but my wife wanted to explore the side streets and shops in Sintra instead.
Having a cab wait for you at Qunita da Regaleira does not sound like a good plan though, I believe cabs in Sintra are very pricey so that would be a costly way to do things..
If you picked 3 or your 4 options I think it will be an easier day but if you skip the shops and downtown exploring in Sintra itself and just hit the sites you could do all 4 on your list in the day, especially with a 9:30 Start time.
We actually expected to be there earlier but our bnb served an incredible breakfast but not starting until 9 AM which we thought crazy late, after experiencing the day before how fresh and good the breakfast was I decided it was worth it to go late to the castle and walk a little more as a result. Our bnb was only a 15 min drive or so away.
Did not see may taxis about, plenty of tuk tuk drivers though and other cute taxi like rides as well as the buses.
Would be easy to catch a tuk tuk outside of the Pena Palace park entry area but not at the Moorish Castle entry. None are waiting around there.
Worst part of the day, was after the Moorish Castle when we walked down to the our car, that road only runs one way so we had to drive up along with all of the other tuk tuks, cars, busses and walkers up to the Pena Palace and then back down again on the one way loop and that was really a painful experience with constant stops on the uphill park and generally little room for the walkers on the road.
Really bad system they have in place, the town should not allow passenger cars on that road and instead have more frequent busses for that stretch ; add pay parking lots to pay for the new bus system would make the experience better and make the town more money.