Can You Shift from 1St to 3Rd?

Yes it is recommended that in a modern manual transmission you can skip gears when going up or down. For example; when accelerating you can if required change-up from 1st to 3rd, though 3rd gear may labour due to low engine revs.

Can I shift from first to third?

Rather than rowing through all five or six gears, drivers will skip from third to fifth, fourth to sixth and so on. But is this practice safe to do? Engineering Explained tackled the common practice in its latest episode and the short answer is yes, it's perfectly OK to skip gears when upshifting or downshifting.

Can you go from neutral to 3rd gear?

Yes, but there is really no risk to your transmission. The clutch maybe, but if you learn to rev match downshift well, that risk is gone too.