Yes, you can fit six #6 stranded THWN-2 copper conductors into a 1" Sched 40 PVC conduit, along with up to two #10 ground wires.
Technically, if you use two stranded/insulated #10 THWN-2 ground wires, your conduit fill will be 40.03%. However I would disregard the 0.03%.
Yes, you are allowed to have all these wires stop at a junction box and get spliced to continue onward. If you split the ground wire to both the garage and hot tub, you only need one ground wire.
However, it will be a big box. Each #6 wire needs 5 cubic inches. You will have 6 from the house, 3 from the hot tub and 3 from the garage = 12. Plus 3 cubic inches for all the #10 grounds. So the box must be 63 cubic inches. Now you'd think you could get that beast at a big-box store, right? Nope. You'll need to go to an electrical supply for big boxes, and while you're there, check their prices on other stuff. I find big-box stores are only cheaper on the most popular commodities; on everything else they are a blatant ripoff.
You must use actual white or gray wires for neutrals. The upside of that is that black/colored tape markings on white wires have no meaning whatsoever. This means you can use colored tape to distinguish the two circuits. For instance I might use all black and white, and mark 2 hot tub hots and 1 hot tub neutral all with blue tape, and the garage circuit with red etc.