As for the second part of your question, you can't directly relate equatorial/axial to dash/wedge, since cyclohexane can freely flip its ring, which will change the equatorial/axial position of a substituent on the ring. However, when you have more than one substituent on the ring, you can make a distinction since their relative positions do not change. Here's how it goes:
1,2: axial-axial = trans, equatorial-equatorial = trans; axial-equatorial = cis, equatorial-axial = cis
1,4: axial-axial = trans, equatorial-equatorial = trans, axial-equatorial = cis, equatorial-axial = cis
1,6 (same as 1,2): axial-axial = trans, equatorial-equatorial = trans, axial-equatorial = cis, equatorial-axial = cis
1,3: axial-axial = cis, equatorial-equatorial = cis; axial-equatorial = trans, equatorial-axial = trans
1,5: axial-axial = cis, equatorial-equatorial = cis; axial-equatorial = trans, equatorial-axial = trans
basically, 1,2 and 1,4 axial-axial point away from each other so they're trans. 1,3 and 1,5 axial-axial point the same direction so they're cis. Ring flip changes axial to equatorial and vice versa, but doesn't change the cis/trans spatial orientation, so 1,2 and 1,4 eq-eq is also trans and 1,3 and 1,5 equ-equ are cis. Swap on of the substituents from axial to equatorial changes the stereochemistry from cis to trans or vice versa.