I've never seen a table of direct conversions but I've included tables of wire gauge in millimeters and needle size in millimeters. They aren't exact matches, but you may find matches that are close enough for your purposes.
You didn't say if you are talking about U.S. size or UK size. U.S. size #10 is 6.0 mm where UK size is 3.25mm, which is a considerable size difference.
Gauge of a sample is determined by how many stitches can be made within a certain designated number of inches. You can't know that without knowing the yarn being used as a fingering yarn will make more stitches in 4" than a worsted weight or chunky yarn. Also, the pattern stitch will make a difference.
For example, a pattern might say Gauge: 26 sts = 4" 20 rows = 4". You would have to make a swatch, then measure your stitches to see if you get the required 26 stitches and 20 rows in 4" if you want the item to be the same size that the designer specifies. If you get 26 stitches, but not 20 rows, then you have to adjust your tension or stitch height.
If you are using fingering yarn you might get more; if using chunky yarn you might get less with the same needle.
a 14 or small 16
needle- is used for sewing.
It depends, sewing needles come in all different sizes.
It is a sewing needle.
It is a sewing needle.
Sewing
A packing needle is a large needle used for heavier sewing, such as for sewing up canvas packages.
No but the sewing machines thread the needle for you will help.
NEEDLE
If you use a thimble, it can help prevent sewing needle pricks.
Yes, a sewing needle is a conductor of electricity, depending on which metal it is made of.
A sewing needle needs to be very sharp so that it can penetrate the fabric which it's sewing with ease.
A sewing needle needs to be very sharp so that it can penetrate the fabric which it's sewing with ease.