Normally I would just reply privately for you but I think this is something people could relate with, especially with summer coming up.
I’m not so sure about arm warmers, I think they tend to look a bit funny with Lolita to begin with but it’s especially hard to see them working with that particular dress. Maybe if they were tall lace gloves, but I’m just not sure about them being arm warmers. How bad is the sunburn? I burn pretty easily and I’ve found that if it isn’t too painful and it isn’t peeling or anything gross like that I can just cover it with some foundation and powder and it will cover it nicely. Most people will recommend putting on aloe vera and letting it dry and then put on makeup after.
Obviously the ideal thing would be for it to just fade though, and I’m not sure if these really work, but I’ve heard a few home remedies that might possibly help. The most popular I’ve heard is to put plain yogurt on your skin after a shower and leave the yogurt there for 15-20 minutes and then rinse it with cold water and apply aloe vera.

What you suggested would be fine to make your lashes appear larger and open your eyes up a little bit, but you don’t have to completely rule out eyeliner. It sounds like you’re talking more about eyeliner that goes above your lash line. Have you tried using it on your waterlines instead? If you want to make your eyes appear larger, line your top waterline with a dark eyeliner (black or brown) and line your bottom waterline with white. The white opens your eyes up while the black makes your lashes look fuller. Add a little mascara and you’ll define your lashes and open your eyes even more and you won’t even have to worry about any eye shadow.
If you wanted to look at other techniques you might be able to experiment with, there are a lot of different tutorials here.

I know Dolly Wink is recommended very often, and they name their products so you can look them up and find reviews and pictures of what they look like. Pretty & Cute also carries a lot of great brands that you can find reviews for. I don’t use false lashes very often so I can’t say for sure what the best would be, but there are plenty of reviews around for different brands so you can see what they look like and decide for yourself.

That depends. More subtle and casual Gyaru makeup such as what you might see on Liz Lisa models will usually work just fine. However if you were thinking more along the lines of Manba makeup (which I don’t think I’ve actually seen for several years now so I don’t think it’s all that popular anymore anyway?) or something super outlandish like that, you might want to stay away because it’s pretty far off from the Lolita aesthetic. I’m not exactly up-to-date on all that is gyaru, but basically just use common sense and choose a makeup style that suits the Lolita aesthetic.

She meant it to be for costume purposes and I’m glad she said something about that because it really isn’t something for just everyday wear. If anything it could be used for a photoshoot, but not all that much more. I don’t think she really has all that much knowledge about Lolita so it looks more like costume makeup than anything.

As long as the color looks good on you and makes sense with the rest of your makeup it can work perfectly well.

Not necessarily. Some people just don’t look good in blush. I think it’s definitely something you can experiment with to see if it works for you, especially with Sweet Lolita because it helps give a cute and girlish look, but if you don’t like how it looks on you, don’t wear it.

It’s often a little bit of both. Usually if they’re candid pictures or meetup pictures it’s just really good makeup and skin care and if it’s from a photoshoot or a magazine it’ll be makeup plus some editing (sometimes people will go overboard with the editing though.)
Don’t rely on Photoshop too much though because no matter how hard you try, even if you edit every picture you take of yourself, you can’t Photoshop real life and I’ve seen Lolitas who look completely different in real life than they do in the photos they put on the internet.
So, if you really want to obtain flawless babydoll skin without Photoshop, there are a lot of things you can do. The most important thing is to just take good care of your skin. I recommend washing your face twice every day, once in the morning with just a washcloth and water to refresh it and then before you go to bed to remove any dirt and makeup. And don’t go to bed with makeup on! No matter how tired you are, just take two extra minutes to properly wash your face with a cleanser that works for you (which may take a little trial and error to find) and I promise your skin will thank you. (Your pillow case will also thank you. If you have a light colored pillow case, sleeping with makeup on just makes it look gross.) Also be sure to drink plenty of water. Your body is made up of mostly water and your skin is no exception so be sure to keep it hydrated. Eight glasses a day is usually recommended. I also recommend looking for a skin moisturizer that you can put on your face at night before you go to bed, especially since you say you have dry skin, and you can also get a moisturizer or cleanser that helps make pores smaller. I would also have a spot treatment on hand just in case. Even if you aren’t overly prone to acne, everyone gets a pimple every now and then so it’s good to have something you can use in an emergency.
Along with taking good care of your skin, a good makeup routine is necessary to get the perfect dolly look you see many on so many Lolitas. For some makeup tips, see this list of tutorials.