This is my personal opinion! I would not use Photoshop Elements on a laptop UNLESS it has a really powerful CPU, lots of memory, and an SSD. I run my PSE2020 on a desktop PC with an Intel i9-9900K CPU, 32 GB mem, and a 512 GB SSD. It is VERY fast! I also have it installed on my ASUS laptop which has an Intel i7-7700HQ CPU, 32 GB mem, and a 500 GB SSD. The laptop runs PSE ok, but not nearly as fast as my desktop.
If you get a laptop with only the MINIMUM requirements, it will run Photoshop Elements, but I'm sure that you will be disappointed with the performance! JMO. Also, BEWARE, most new laptops do NOT have a CD or DVD drive that you'd need to try to install your PSE11.
To answer your first questions, the current license allows you to install Elements on two computers, but you can only use one at a time. I may be wrong, but I think earlier versions allowed installation on more than two computers, but again only one could be used at a time. I'm not sure about Version 11. So you don't need to uninstall the program from your old computer.
As for installation on a laptop, most recent ones don't have a disk reader. However, you can copy the contents of your installation disk to a USB thumb drive using your old computer. You can then install the program from the USB thumb drive. External disk drives are also fairly cheap.
I'm not sure that you need a whiz-bang machine to do basic editing in the Editor, or to create Slideshows. Elements 11 was designed to work well on machines that are now 7 or 8 years old. Pretty much any current machine will have equal or greater power. However, if you intend to upgrade at some point to a current version of the program, it would be best to go for something a little more robust.
I think your question re the specs for a laptop for PE2011 has been answered. But why not take the opportunity to upgrade to PE2020? It's got a lot of new and improved features. (No, I don't work for Adobe; rather I have been impressed by the upgrades Adobe implements every year and I personally have upgraded at least every few years). If you plan to upgrade, I just don't think you need a super laptop. I just bought a new laptop with an i7 10th gen and it's plenty fast for PE2020.
I would, however, make sure you don't underspend on the screen size unless you have an old hi-res monitor you can use as a second screen. I have a 15 inch and I get by but I certainly wouldn't want a smaller screen.