Eyes (in conjunction with eyebrows) are one of the many details which can trip artists up, and I think it's mostly due to how they capture the emotions, feelings and sometimes even character of who's being drawn. Eyes complete the picture where your other facial features (mouth, nose, ears I guess, hair I suppose) set the framework. The style of eye I draw is a bit of a hybrid between a realistic eye and an anime styled eye, but in terms of where to start for you I'd suggest taking inspiration from eyes of characters from Nintendo series such as Mario, Legend of Zelda and Kid Icarus (those with human(oid) characters) and seeing how their eyes work. I don't have time now but when I do I might whip up a really brief introduction to eyes. (I'm still learning the art as I'm not nearly as proficient in expression through eyes as I'd like to be...)
Adapting character design elements to 'make' new characters I suppose depends on a couple of things: (1) a decent ability to imitate or 'copy' - if you check my old art topic you'll notice some drawings seem to be (or I've commented as) being a copy of something I've looked at and then drawn by eye (as in rather than tracing, I've gone and relied on my hand eye coordination to copy). (2) having an understanding of how I intend to portray this new character - this relies on understanding human anatomy (I'm terrible with non human designs) and posing, and both are very very difficult to master (I am certainly NOT one, my dynamic posing is pathetic). Even just having a feel for 'is this character meant to be heroic? Calculating? Contemplative? These can determine how you frame your character. (3) being able to apply features from different sources and then seamlessly combine them - this is more the creative side of things compared with the somewhat scientific way of learning anatomy or perfecting your copying skills.
I guess it's important to figure out how I got to where I am drawing wise. Back when I was a lot younger, I tended to just draw lots of Kirbys - without reference in most cases, and these tended to be me just drawing abilities that existed as well as made up ones. This was probably my creative (point 3) showing through, with a bit of imitative (point 1). I still kinda drew is sort of cutesy thing for a while, but I know Meta Knight came into the picture about freshman/sophomore year. When I hit around sophomore to senior year, I started drawing characters from Fate/stay night, and this was certainly the imitative (point 1) phase. My studying phase (point 2) really just made its way in randomly and was probably from a branching off from copying Fate characters to actually try and make my drawings more 'realistic' and less 'wrong' looking. Point 2 has persisted since, and remains the foundation on which I draw capybara terms now, unless I'm rushing. Point 3 for blending has become more prevalent again as I become inspired by video games and also random suggestions from others, which I then take these ideas and then study them so I can pseudo-imitate them but with my own memory and my own style, rather than purely copying as per Point 1.
Oh also I have done some still life drawing but that was also ages ago, and doesn't have as much impact (still a bit though) when drawing characters.
I guess the important things to say are:
1. It's not shameful to try and copy when you're first starting. Imitation is the sincerest form of flattery, as the saying goes. It's also a learning process - what sort of visual styles you want to imitate, what character designs appeal to you, how do you develop understanding of body proportions, etcetera.
2. Once you learn realistic anatomy, you will appreciate why characters don't conform to that. Mario characters in particular throw realistic proportions out the window (Mario's head is as big as his torso, and Peach has legs that are longer than her head to waist height, for example, but these are choices to emphasize the fantastical and perhaps slightly younger audience tailored designs). It's often a series wide stylistic choice, but if a single character has unusual proportions, the designer wants us to acknowledge this difference represents something.
3. Never stop critiquing your own work. Is it how you hoped it would turn out? (You'll find the answer is very often No.) What could you have done better? Did you make a mistake with the anatomy? The pose? The proportions? Perhaps you drew the clothes wrongly? Their expression isn't quite right? As long as something isn't quite what you wanted, you'll have something on which to improve on. Also ask others for comments, but make sure you know they'll give you helpful tips rather than 'hurr durr ur art sux' because that doesn't help you. For example, in the Toblet image, I know that the feet aren't great, and the hands don't look quite right. But also, her left leg looks rather distorted given the angle she's folding it.