What caught my attention was that you said you're using a MANUAL lens, but you're trying to use different modes (including AUTO).
For any case there are only one, correct mode. Either the one you deliberately choose, to achieve particular effect or the one that fits the situation best, if you're after general outcome.
Depending on the lens type, this can get quite limited. E.g. there are A and M type lenses, as well as even more basic ones. Besides the manual focusing all of them have limited exposure capabilities. Most of them have known exposure errors, related to their mechanics and type of operation.
Before doing anything else, you need to determine what type of manual lens you have. Then see in what modes and what way they function with K-x.
Some manual lenses may have hard to notice defects. Often they are very old, worn, crude. In lenses which are stopped down by camera (non S/m42 type) slow, sticky (oily), jumpy or otherwise flawed aperture blades can cause erratic exposure,
Was it the same with kit lens as well? Then there might be some other thing to look at...
Another note. I've repeatedly noticed that in very bright sunlight you must take great care to completely cover the viewfinder eyepiece. If you don't press the camera fully against your eye, light will enter the camera from both, lens and viewfinder. Since exposure reading is taken from focusing screen, additional light can decrease the exposure by as far as -1EV. Thats as much as I've observed.
I must also agree to other members about the harsh light conditions and time of the day. Btw, manual lens most likely would not work with high end high-speed-sync flash either.
If you already have taken note on the above suggestions, there might be some other flaw or issue (forgotten compensation setting, limiting setting chosen - e.g. often i forget too high iso, like 400-800 and with 1/4000 shutter speed and lens at f/16 camera has no more options to make the picture darker). Even with quite ugly exposure variation and problems it is hard to get images as blown as the last one. If its K-x and everything else was ok, the camera might be faulty.
Good luck and hope this helps. More technical details are welcome (e.g. exact lens model, exif data of the images shown).
Yay! This is my 1000 post!!! Must have cake
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