You can put any Dimensions mini-figure character on the Dimensions portal pad at any time in the game, and then you can use that character in the game immediately.
For the vehicles and accessories: "Level Packs", "Fun Packs" and "Team Packs" work slightly differently for these:
- To build and first use a vehicle or accessory from a "Fun Pack" or "Team Pack" just place one of the characters from that pack on the portal and switch to using that character in game, the game should then immediately pause and you be prompted to build the vehicle/accessory using the on-screen build instructions and then write it to its tag.
- However, to build and first use a vehicle or accessory from a "Level Pack" you need to play through that Level Pack's level and at certain points in the story of that level pack you will be prompted to build the vehicle or accessory by following the on-screen instructions and then write it to its tag.
Once you've built a vehicle and written its tag, you can place it on a Dimensions portal pad at any time to use it.
To answer the "vehicle modes" question that you alluded to in your last sentence: All vehicles and accessories have an initial mode (instructions to build and unlock the first mode will show when you meet the conditions above). Once you've built the vehicle's first mode then, whenever you're in the hub world, you place the vehicle's "owner" character onto your physical portal, and then walk the in-game copy of that figure onto the same (glowing) pad on the hub world's in-game portal. Then press the button corresponding to the icon that will appear above that character's head and you should see a menu appear, one item on that will be "Upgrades" select that and you can spend your collected Lego studs to buy vehicle upgrades across a number of categories. Once you've bought enough of these upgrades you'll see that the icon for the second (or third) mode of that vehicle which change to show how many Gold Lego bricks you need to spend to unlock that vehicle mode.
Once you've unlocked extra vehicle (or accessory) modes, you can switch between them on the fly by getting into/onto/picking-up that vehicle/accessory and pressing your action button (B on XBox or Circle on PS4) and selecting the vehicle mode from circular menu that pops up.