Is it safe to design board at fab houses minimum trace width?
A reputable PCB house will solidly deliver their minimum standard track &amp; spacing. 

Some will let you try finer at your risk and some will reject your work outright if under spec.

I assume that you are using a temperature controlled iron. If not, do.

If you are not confident in your own soldering abilities and you have plenty of room then fattening up tracks and especially pads associated with through hole parts does no harm. I'd give the through hole headers as much copper as you reasonably can - especially if the board is NOT PTH (plated through hole). With PTH you get substantially more strength. If the board is single sided (probably not, but ...) then you want to take great care with through hole pad soldering and due care with everything else. 

SMD part pads should be suited to the part and you have to learn to accommodate them rather than them accommodating you.

PS: Others feel free to contradict or improve anything I've said. I have very substantial soldering experience but there is always good stuff and ideas to learn. 
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Related: This excellent reference -
TI Analog Engineer’s Pocket Reference - 4th edition
as well as a vast amount of other useful material
it provides some useful information on PCB track current/ voltage drop / heat / fusing issues. Especially pages 55-68.