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Unless the maple leaf mulch is very thick and heavy, it shouldn't deter your plants from spreading. Are the leaves matted down? That can prevent water from penetrating into the soil. You can buy an inexpensive rake that is not very wide, such as shrub rakes, 8 or 12 inches wide, and fluff it up so it is not matted. Or you can use the small rake to remove some of the leaves to prevent matting.
Tulips come in all types and sizes, so unless you bought the exact variety of tulips bulbs your neighbor did, yours could be a different height.

Here is more about mulch:

https://www.gardeningknowhow.com/garden-how-to/mulch/mulching-with-leaves.htm

Yes, you can, but remember, the bark mulch will decompose over time and the rock mulch will show through. You could rake off the rock mulch if you want the benefits of bark mulch. Here is more:

https://www.gardeningknowhow.com/garden-how-to/mulch/choosing-garden-mulch.htm

Red cedar mulch would be the best out of those three, although all of them carry their risks. The other two can be used, but I don't recommend them. They tend to cause more issues than they solve.

With cedar chips it is important to know that it will tie up nitrogen and cause the soil to be acidic. Supplementing nitrogen and adjusting pH will be necessary. The more decomposed the better, though.

If you have access to aged hardwood chips, like oak, then these would be the best option. Compost is another good option.

This article will offer more information on proper mulching practices:

https://www.gardeningknowhow.com/garden-how-to/mulch/spring-mulching-tips.htm