Introducing New Fish

I'm an experienced goldfish keeper (goldfish kept on their own) but new to tropical fishkeeping. I've had 6 x-ray tetras for 8wks now in a 60cm tank, and they are sometimes incredibly lively, chasing one another round the tank, and sometimes much more quiet, which in itself seems normal. They seem to have become very nervous during water changes and will cower in a shoal behind a plant or in the rock cave, behaving as though terrified, and this tends to last for at least 24hrs, despite the water change only being 15-20% every 5 days or so now.  Also, I changed the location of the filter and heater to maximise the filter output and this again stressed them out for a few days, and they have begun swimming much closer to the bottom of the tank since then although I don't think that it's to avoid a strong current. I was planning to add 6 panda corydoras to the tank but wondered if (i) the panda corydoras would be alright given how lively the fish sometimes are when chasing one another, especially if low in the tank, (ii) there will be an element of competition for space with the x-ray tetras feeling as though they have intruders given that they have had the tank to themselves for so long and now seem to be inhabiting the bottom section of the tank, (iii) the x-ray tetras might become even more panic-stricken if they are joined by new tankmates. Grateful for any thoughts/advice; many thanks.

I would definitely get a few more tetras which in itself should make them feel more secure. Also, do you have quite a few plants in your tank? If there's lots of cover they're likely to feel more comfortable out in the open if they know they have somewhere to go if they need to.
I've kept panda cories in every tropical tank I've ever had and they have never, ever caused problems for me. My cories have always been pretty active, constantly playing with one another and searching for food at the bottom of the tank so if the tetras are boisterous I doubt that'll worry the cories at all. I shouldn't think that the cories would spook the tetras either because they tend to stick to themselves for the most part, but I'm not 100% sure about that.
I don't know how much you know about cories, but they really need to be in groups of six or more. In a 60cm tank I would have about eight. They do require their own food; I just buy them sinking shrimp pellets which they really love. They also prefer a sandy substrate to gravel. I know you've already set your tank up and I'm assuming you've used gravel which is okay (all of my tanks have had gravel), just make sure the gravel is really smooth because any sharp edges could hurt the cories. In some of my tanks I've kept a little dish of sand in the aquarium and some cories have really enjoyed playing in that, but it does create quite a big mess and you have to be careful when you're gravel vacuuming to make sure you don't suck it all up. 
Hope that helps

Gosh that looks really nice- I especially like your driftwood! That sand looks to me to be okay, but maybe someone else here has used it and would know for sure

Thanks - that's helpful too; I had actually thought it was overcrowded with accessories, so I'll get 'on the case' with finding some additional hiding options for them.

Thanks; that sounds an excellent idea to have higher growing plants and might also address another issue which I've noticed in that the fish seem to be more likely to swim higher when the light is off so perhaps they find the light too bright for them and some more 'shielding' from it might help.