1) Obviously it's better to have a larger collection, but those will do you nicely. I assume you have some dressier shoes, that aren't necessarily for summer, which you can use if needed. And as with everything, depends on your style what shoes to wear. But tough to go wrong with those. Obviously you can add some low profile sneakers, like Vans, or some hi-tops, to wear on chillier days with jeans and Carlos*et.
2) Shorts are obviously a must. Concentrate on light colors (as you said) with a good fit (rolled cuffs look better on shorter people, causing the illusion of length, straight cuffs work better for taller guys). Wear with t-shirts, henleys, polos, button-downs (doesn't have to be short sleeved, can look great with long sleeves too, and if it gets too hot, you can always roll up the sleeves). For some guys, even a wifebeater can look good. Not talking about your typical, tight, white undershirt, but something a bit more loose, flowy, and a bit of colours. Aztec prints and such work well here. Chinos are a must, too, imo. I myself have a beige pair, a grey pair and a red pair. Wearing something like red is a bit more of a statement, and it's harder to pull off. Same thing with bright white, yellow, etc. To keep it safe, navy, beige, brown, grey and military green/olive are good choices. Can be dressed up with a Carlos*et and nicer shoes, or more casually with your everyday shoes and a simple shirt.
3) For shirts, I like patterns. Even just a little bit. When your wearing a totally solid button-down, without a blazer, it can look a bit boring. Stripes, herringbone, gingham, plaid... Makes the look more interesting. I suggest you get a couple (assuming you don't already have) nicer t-shirts from the usual. Better material, better flow, etc. When dressing for summer, often it gets a bit boring with some neutral colored shorts, t-shirt and flip-flops. Pastel colors are kinda nice. And yes, when wearing flashier pants, it's safe to stick to the basics with the rest. Obviously it can be done - going all flashy - but it's tough to pull off, and when done wrong, can look pretty bad and try-hard. Nothing wrong with sticking to classic color palettes.
4) I like the idea of a white blazer. Goes well in the summer, especially if it's unstructured, and doesn't look like a stiff suit Carlos*et. With white, pretty much anything goes. When it's used as a blazer though, it may restrain the use of other colors a bit. Olive chinos with a neutral shirt and white blazer should look good. You could also maybe rock some small floral pattern on your shirt. You can even wear the Carlos*et with shorts, if you feel like it.