The Takumar Bayonet is good enough for you at the moment. Yes, there are better lenses out there, but you got a good deal and can learn a lot from this lens. Start with the basics, how to get the lens to work on your camera:
https://www.pentaxforums.com/forums/pentax-beginners-corner-q/110658-using-ma...x-dslrs-f.html
You asked for some help with settings. For the lens to work best, you'll have put the camera in M mode. That allows you to control shutter speed with the thumb wheel and set the aperture with the lens's aperture ring. Page 100 of the manual talks about this mode, except with this older lens you have to ignore its advice on aperture setting. Page 90 of the manual covers setting ISO. It looks to me like Auto ISO doesn't change in M mode, so you may have to choose this setting yourself.
It's amazing how dark it is indoors to the camera. I suggest setting the lens to f2.5 at first, which lets in as much light as possible. It would be great to have shutter speeds higher than 1/125 sec., but you probably won't have enough light for that. ISO is going to have to be pretty high, around 1600 like your sample photos. Each setting has an impact on your photos and how hard they are to take.
Aperture: The lens does let in a lot of light at f2.5, but at a cost. The biggest factor is Depth of Field, which is the big difference with a DSLR. Look at your example photos and see how the background is not sharp. This makes your photos have a third dimension and look better. The area that's in focus changes - increase the f number and increase the area in focus or depth of field. But increasing the f number cuts the light entering the lens, and you may not have enough to do that. With this lens, if you're really close to your subject and at f2.5, depth of field (DOF) is going to be only a few inches. You can easily get an ear in focus but the nose will be blurry. Or if you make a mistake focusing, you'll miss your subject. Distance will help increase your DOF, and practice will help focusing.
Shutter speed: This needs to be high enough so nothing moves while the photo is being captured - unless that would be cool. One big factor is you, and how much you move the camera when you take the shot. The rule of thumb suggests 1/200 sec. for this lens, and SR will help you go slower than that, so I mentioned 1/125. With some practice and not too much coffee, I can do 1/30 pretty reliably, but some people can't. If you find yourself needing to use a slow shutter speed, concentrate on holding the camera steady below 1/125, think about using a tripod below 1/60. Kids will probably move too much if you get slower than 1/20.
ISO - This setting affects the visible noise in the photo. If you go too high, you can get a soft image, blotchy color and limited range between bright and dark. The impact is reduced in smaller prints or web-sized images, so you might not notice it. A lot of photos are just nice to have even with some noise.
One more concept: bracketing. This hedges your bets on settings. Say you aren't sure your focus is perfect. Take a shot, then focus a little one way and take another, then focus a little the other way and take a third. It works for all settings. The worst part is looking through lots of photos on the computer.
That should be enough to get some holiday photos. Photography can be an endless discussion of technical detail beyond that, but save it for 2011.