Could you describe the tank you have? Size, water level, lighting, filter etc?
The picture you have is either of a map or some type of slider. Either way all turtles (except some softshells) bask, especially the maps and sliders. It is totally normal that the turtles don't bask the first few days in a new set up they just have to get used to it, as for the swimming against the glass thing, mine still does it after a year that I've had it they are incredible beggars
If you do not have a basking/heat lamp please get one as soon as possible, it really doesn't have much to do with the current temperature in the water (That''s what the heater is for) it is just a source of heat as turtles are cold-blooded and also a way for the turtle to get dry. You have to make sure that the turtle will be able to take it's entire body out of the water to bask
Apart from the basking light, you also need a UVB light over the basking area. This will provide calcium and rays of light that are beneficial in the growth of your turtle as well as the health of your turtle and it's shell! You absolutely need to make sure you have both of these lights. The heat light bulb can be bought just about anywhere and is a regular spotlight bulb like the ones used outside. As for the UVB light, I would recommend the lights from Zoo-Med 5.0 or 10.0 depending on the size of the tank, and it is the best provider of UVB (10%).
Could you maybe add some full tank shots as well?
I wish you well with your turtle!
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