Tp answer your question about a "remote" shift, it was an early style of shifter, after the original style "pudding stirrer".  The remote shifter used a cast aluminum extension bolted to the back of the differential housing. Inside the extension was a horizontal rod that linked to two other smaller rods to convert a forward and back movement and a twisting movement to similar actions inside the gearbox that the gearbox shift components could understand. Ut was slightly less vague than the pudding stirrer And my description.

 

Your rod change shifter uses a straight rod coupled to the gearbox shift mechanism, making the actuation much more direct. It also has a second fixed rod to keep the distance between the gearshift lever and the gearbox constant. 

The axles are the same. You should have pot joint output on your rod change gearbox. The upper coolant hose is different from 998 to 1275. The starter and motor mounts are the same.

So, I'm getting a full package with electronic ignition, built gear box with stage 2 clutch, carb and intake manifold as well. The things I'm wondering about are: are there any changes to CV axles, coolant lines, starter, motor mounts, what is remote shift? Are there any common fitment issues switching from a 998 to a 1300+? From what I understand it's a simple swap but I always assume everything is to good to be true.

Thanks!

You should be able to use most everything in the switch over. Would want to check the carb size as it may be a 1 1/2". It would work but a 1 3/4" would be better. Will also need an intake manifold and exhaust system. A LCB, long center branch, exhaust is what most folks end up going with. New water pump as they are cheap. Look at the inside of the radiator to see if you want to change it. The inexpensive aluminum ones on ebay work well. Change the lower hose as it is not something you want to do with the engine in. Hook up the speedo cable before you drop the new engine all the way in. While the engine is out check the condition of the front flex brake lines. now would be the time to change them. If your mini is an Inno you will want to use the gauge sending units , oil & water, from the old engine so the gauges will read right.

See how this snowballs.

The current engine is an original 998 to the car.

Sounds like you're swapping one A+ engine for another A+ engine. In this case almost everything should be compatible. The parts you intend to reuse will need to be inspected to determine if they require replacement. It's likely that these will be the bulk of what you need to buy. It's often best to replace the clutch unless you plan to have it apart again in the near future. 

On '80s and '90s Minis the best initial steps you can take for handling is to replace the rubber subframe mounts with the solid type  and find lighter wheels and tires.

Kelley 

Keith Calver has a lot of well written info on his website. https://www.calverst.com/

Look in the "Technical Info" section. Covers engines to suspension and all in between. Plus he sells some nice parts.

Having a 1330 fast road engine built for my 91 the new engine is an A+ all balanced stage 3. Trying to figure out what accessories will swap over and what I will need to buy any help will be appreciated! Also any info on making the car corner better would be helpful! Thanks!