tomaja

I should be working, at least it did when I was checking with Google Chrome Inspector. Your slider images are now within normal size, no more gap ?

This can be done by changing values for line-height, but you must be carefull because slider is resposive (for better adapting to different browser sizes), so you must include @media queries to make your change work on all screens. For smart phones this is the default Customizr css code where you can change height values in px

@media (max-width: 480px) {
  .carousel .item {
    line-height: 190px;
    overflow: hidden;
    min-height: 190px;
 }
}

and for big desktop screens

@media (min-width: 1200px) {
.carousel .item {
    line-height: 500px;
    overflow: hidden;
    min-height: 500px;
 }
}

I suggest you read this snippet that explains this much better and in details.

Do you use default slider that comes with Customizr or some other ?

This is an option integrated into theme menu. To change size of the first letter you need to add

.navbar .nav > li > a:first-letter {
font-size: 42px;
}

This has nothing to do with Customizr theme. You should post it on the widgets support forum.

Your featured images should be 270×250 in size. Check this page about specific image sizes.

You could use this snippet, by changing link to fit your needs, e.g. adding few classes for button