It looks like your seatpost clamp is a quick-release, similar to the quick-releases on your wheel hubs? If so, you can tighten it the same way as you do the hub QRs - release the lever and turn it. It should be normal thread (righty-tighty, lefty-loosey). You may have to play with it a couple of times to get the right tension on it to where it's not so tight that you can't close the lever, but tight enough to hold.
As for pumps, do you have a true mini-pump, i.e., one small enough to fit in a jersey pocket, bore of a half inch or so? That kind is basically only good as a back-up to a CO2 inflater. You can inflate a tire fully with that kind of pump, but it will take a loooooooong time (and high-pressure skinny tires take a lot of strength, too). For general on-bike use, you want either a full-sized frame pump (big enough to inflate a tire reasonably quickly) or a CO2 system with a mini-pump as backup if you run out of cartridges.
A floor pump is MUCH quicker and easier to use than a handheld, plus many floor pumps incorporate tire gauges, which is why it's better to have a floor pump at home for topping your tires off.
Also, bicycle tires can have two different types of valves. Fat-tire hybrid bikes like yours usually have Schraeder valves, the same type that motor vehicle wheels use. Skinny road bike tires usually have skinny springless Presta valves. Make sure your pump is compatible with the valves on your tires (most, but not all, pumps will handle both; some pumps require you to reverse the head or flip a switch, and some claim to fit both without making any adjustment).
HTH ... and welcome!