It is not a good idea to put a swap partition on a usb drive. usb drives can be written to a limited number of times (thousands) and then they fail. Having a swap partition will mean that it is written to a huge amount, so it wont last very long.
You decide whether to have persistent /home and /opt. If you do, this will also shorten the life of the usb drive. The other option is to use backup. However, this may result in taking a long time to start up and shut down, depending on how much you have in backup. You could use persistent /home and /opt, and just replace the usb drive when it fails.
I will explain it another way. If you use persistent home and opt, every time you save something, it is written to the usb drive. (If you use Firefox internet browser, it writes a lot of cache to the /home directory, unless you change settings.) If you use backup, when you save something, it is saved to ram. It is not written to the usb drive until you run backup, normally when you turn off the computer.
Use ext2 filesystem. This is not a journalling filesystem, and the usb drive will last longer.
If you use Grub, or most other bootloaders, the usb drive may be sda1 in one computer, or usb slot, and sdb1, sdc1 or sdd1, in another computer or usb slot. So you can't include anything in the bootloader with reference to the partition. For example, you can't have tce=sda1. It can be used this way. Tinycore will find the tce directory. It is just not ideal. You can't have persistent home or opt. If you install using the HD/USB install in Tinycore's control panel, it will be identified by its UUID number, using extlinux. This is the same in every computer, so you can have tce=UUID number. You can also have persistent home and opt. I suggest you install one using this method, just to see. But I don't know how to install it like this and set it up to duel boot. You could research this. There may also be others that know.
FAT32 needs to be on the first partition if you want to access it with Windows. Windows may not be able to access any other partition.
Windows operating systems need the partition to be Active or Boot, in order to start the operating system. In most situations (not all), Linux does not. You can only have one Active partition on a drive.