NO NO NO NO NO do not start on anything like that. That's a HUGE moputhpiece that takes a lot of support to handle, and it takers time to develop that kind of support. The diameter of the mouthpiece should be fitted to your mouth. It is more your facial cavity and the mouthpiece's depth that influence the sound anyways.
A 7C is a decent starter mouthpiece, and a 10 1/2C if that feels too big. Really, everyone's face is different. I personally play on something approaching a 10 1/2C (I play Warburtons and Yamahas and Reeves mouthpieces).
Also, it looks like the mouthpiece shank (the tapering part) is wrong for that horn - it looks too long. Go to a reputable music shop and have then recommend a mouthpiece for you.
Now, for your slides, I would suggest KY. Vaseline gums up your horn.
A good valve oil is essential. You oil your valves (which should be numbered as mentioned above). I lube my tuning slide (the big one farthest away from you face) and my second valve slide with a heavier lube . I use a light piston oil on my first and third valve slide because those need to slide in and out quickly, especially for low C# and Ds.
For stuck slides, I use a short towel as mentioned above, and also gently rock the slide everyway I can.
Sweet deal on the horn, BTW, have fun with it, and give me a shout if you have any questions I can help with.