I recommend putting the outline on a similarly-scaled Earth map and see how things compare.

As to whether moving the mountain range would affect the local climate, it will depend in very large part on the local wind and ocean current patterns. A suitable set of patterns can ensure that the mountain position doesn't make a particularly large difference. One thing that you'll find is that enormous oceans result in much more violent storm patterns because storms can just keep gathering power until they hit land. Having a mountain range on the southern side might make things moister than they are now. Because those mountains are fairly far from any coast, they may or may not have a huge impact on rainfall patterns as they are. Again, I am not a climate expert.

I used the term "dead mountains", which is not quite correct. I was referring to the entirety of the mountain change on the continent (both 1 and 2, but mostly 2) and describing what happens when a large mountain range is pushed up in an area and then the plate cools, locking the plates in place and leaving the mountains to slowly erode away. On Earth, there are some good examples of this sort of pattern, including the Appalachians (and their other fragments in Europe and Africa) and the Ural mountains (look at those for inspiration on basic heights and local landform shapes). In both cases, there was a massive collision that uplifted huge mountains and then the uplift stopped, locking the plate boundary in place. How well that would play on a world with only a single rather small continental mass isn't something that I can say much about. A lack of continental masses can imply either a hot world with lots of smallish, fast-moving plates; a cool world with its last hurrah of plate collisions happening with everything else eroded down to just below sea level; or possibly a world that's had a recent deposit of a large amount of water (perhaps a large storm of small comets) that raised the sea level by a few hundred meters and drowned the other masses.

If the larger continent is the result of an older plate collision, then the range down the middle of it is more likely to be set of parallel folded mountains rather than a single block. The fusion would result in what is acting like a single plate at the moment, with the smaller mass to the upper left being a separate plate that subducting under and uplifting the main mass. You would expect to see some mountains parallel to the new collision/subduction zone, which you have on the smaller mass, but not the larger.

The nice thing about having a map serve a story is that the map is useful for keeping a sense of scale and for inspiration. Unless your story is one that is specifically about the tectonics of the map and how they play out over time (for example: the continents are sentient and the merging of the two older ones and how they deal with the impinging of the new continent is the point of your story), then it's unlikely that the tectonics will be more than a backdrop against which the rest of it plays out. Putting your desired map on an Earth map of similar scale and latitude can get you sufficient plausibility for most stories. How a single continent would work on a mostly-water world with minimal ice caps is something I can't answer. The Earth designer chickened out in the design phase by putting solid attachments for polar caps in place, so worlds without such anchorages are a matter of speculation (ocean currents might distribute heat poleward well enough to prevent things ever getting much colder than England, but without the need for a tiny and hot Gulf Stream).

Based on the positioning of the mountains, you might find good models along the west coasts of the Americas more easily than the old world. You're looking at something the size of Australia, so you might look at that area as well (think flipped upside-down and being a bit colder).

Also, I would expect there to be a lot of rivers as it stands due to likely increased precipitation from lack of other land masses. With higher mountains, you'll get even more snow catchment and more rivers.