Hi Kered, welcome to Singastro.
There are a lot of things to know about telescopes, eyepieces, optics, astronomy etc.. so it is not easy to tell everything and to understand everything. It would be best if you can join those group sessions here in Singapore as you would learn more about astronomy and equipment.
What's the difference between a 1.25 and 2 inch eyepiece?
The 1.25inch and 2inch eyepieces denote the barrel of the eyepiece. The telescope has af focuser which accepts 2inch or 1.25inch eyepieces; depends also as some focusers or diagonals are just 1.25inch capable. These are standard USA dimension for eyepieces. Anyway, because of the barrel size, it restricts the amount of True Field (meaning the actual field or area of the sky seen). 1.25inch barrel is smaller than 2inch so 2inch eyepieces have the potential of having a larger field seen.
True field of view (TFOV) = Apparent Field of view (AFOV)/ magnification (M)
The TFOV is the actual area of sky that is seen through the eyepiece.
Magnification (M) = Focal length of telescope/ Focal length of eyepiece
Magnification is the number of times the image is enlarge. 7x means 7 times larger as compared to what is seen with our eyes only.
Apparent field of view (AFOV) is the "circle" you see when you look through the eyepiece. The larger the "circle", the larger the apparent field of view and hence more sky can be seen. For example a Plossl eyepiece has about 50 degree AFOV while a Televue Nagler Eyepiece has 82 degree field of view. The area of the circle in the Nagler eyepiece is 82^2/50^2=2.7x larger than the area of the circle in the Plossl. This means, with the Nagler eyepiece one can see 2.7x more field relatively to that of a same focal length Plossl eyepiece. The larger the apparent field of view, the more immessive it is because the circle is larger and you will feel less 'constrained' as looking through a small circle (like a pinhole).
If you're looking through an eyepiece with a short eye relief, don't your eyelashes get in the way? How do you deal with that?
For these eyepieces, the only way is to clean them or buy other eyepieces that has longer eye relief. Usually eyepieces of short focal length (and hence higher magnification) has shorter eye relief. There are some that has longer eye relief at short focal length but they tend to cost more.
Why are some eyepieces so much more expensive than others (eg. TeleVue)?
Astronomy equipment like in many other equipment has a price. There are reasons why things are more expensive. For example, a ferrari cannot be priced as a Toyota and the price difference comes with different performances or features. Televue eyepieces have many different models. The widest selection of eyepieces compared to many other brands. They are expensive because of build quality and ability to have good images at fast scope like f/4. Slow scopes like those of f/10 can do without such eyepieces but of course these eyepieces will do even better in a f/10 scope. There are other brands like Pentax that do well at fast scopes.
Are there any other characteristics of eyepieces that I should know about?
There are a few things you have to know before purchasing:
1. Get more information about the eyepiece like reviews etc...
2. Know the AFOV and TFOV
3. Know what telescope you have
4. Know your eyes whether you have astigmatism etc.
5. Know the eye relief and whether you are comfortable with the short eye relief of some eyepieces
The best way is to join observing sessions so that you know exactly what kind of astro equipment is out there.