Absolutely. You should definitely repot. You're right about the four signs and I think most of the people are right in their observations. Bamboo always has good advice.
The reason I suggest you repot any new plant immediately is that you don't know what kinds of crazy things are going on in the pot. I'm coming at this more with my orchids in mind, but I've seen it in regular house plants as well.
Here's an example. I almost lost a plant once, because while I watered it regularly, it couldn't access it. The grower had grown the plant in a super cheap and flimsy plastic pot. When they wen to sell it, they just stuffed it in a larger pot and stuffed good looking potting soil around it. My watering was hitting that inner plastic pot and directing the water around it. So it was dying of dehydration.
That's a common practice with phalenopsis orchids at big box stores. They jam a junk grow pot in a decorative pot. Especially, those just add ice people. They actually recommend putting ice on your tropical plant. So don't trust a grower to be looking out for your best interest. Some are great, but some want you to buy a new plant so they can make a profit. That's why I don't take a chance and repot all new plants. That way I know what I'm working with. It also resolved issues mentioned above like soil that is depleted.
The thing to keep in mind as a new plant owner (congratulations and welcome to the hobby by the way) is using the correct type of soil for the plant. For instance, I'm not exactly sure what that succulent plant is with the white stripes, because succulents aren't really my specialty, but it looks like tiger aloe maybe. That type of plant stores water and you've got to be careful not to over water it. You can rot the roots and then the plant will start drying out. You'll water more, thinking that it needs more, but in reality, the roots are rotted and gone and it can't absorb that water.
For succulents and cactus, you can buy a soil specifically for them from a big box store. I mix my own because it's cheaper. I just use my regular miracle grow, and mix 3 parts of that, to 1 part of perlite, and 1 part of play sand, which I get 50lbs of for about $4 at home depot. This soil is very well draining and doesn't easily compact. For the others I'd just use something like miracle grow till you start researching more about your soils. I've always had success with it, though I've moved into composting and worm casting and mixing my own soils.
What I suggest, with you being new to plants, is what I did when I started out. Look up the names of your plants and research the ever living mess out of them. Look up where and how they grow in the wild. Do they grow in shad under trees or in full sun. You see a lot of ferns in the woods under the shade of trees. You also see a lot of them near creeks. Thus they like to stay damp, but not wet. Most, but not all plants dislike being "wet". It's something you'll develop a fill for. An exception that comes to mind are my carnivorous plants. They like to be swampy.
Look up youtube videos and articles on caring for that plant. Be prepared to find contradictory information. :) Just pick what makes sense and experiment. The best recommendation I can give you is to get multiples of any plant you haven't cared for before. Don't put all your eggs in one basket. Say you have 3 plants. You've got them in the shade. You keep two in the shade and move one into full sun. It gets burned and dies. You hate it, but you've got two left so it's whatever. You move one of the others from the shade to morning sun and shade the rest of the day. It does well and puts on new growth, so you move the other one up and it does just as well. Then you hold your breath and put one of them in full sun half the day or even all day. Maybe it dies or maybe it does even better. Either way, you've learned something. You've learned that it either likes full sun, but you need to let it sit for about a week at each increase in light level so it can handle the change, or else you've learned it's not a full sun plant and likes mostly shade, but can tolerate morning sun. You'll keep it there and it'll grow and multiple and within a couple of years, you'll have it stuck all over your house and will be giving the babies away to friends.
So those are my reasons as to why I think you should repot. Also, as a bonus, here are some almost indestructible beginner plants for you to try. Spider Plant, Sansevaria(mother-in-law tounge), peace lily, and (drum roll) the most indestructible plant you can grow in almost pitch black with spotty watering, Pothos! Good luck.