Uneven stitches while machine quilting.

The needle will probably zig-zag, but No the machine generally will not sew sideways unless it is stitching embroidery. To sew sideways, you can use a darning foot or free motion foot, lower the feed dogs, and manually move the fabric sideways as it stitches (see free motion quilting).

https://wpt.org/SewingWithNancy/Video/free-motion-quilting-beginners-part-1

When stitching together a quilt sandwich, it is recommended to use a walking foot on your machine. The walking foot moves the upper fabric in conjunction with the feed dogs. Sometimes, if the quilt sandwich is not too thick, a roller foot can also help but may not be sufficient for a quilt sandwich.
What is Walking Foot Sewing Tips for Beginners
How To Use Walking Foot
How to Use Roller Foot

You may also check the presser foot pressure on your machine. This regulates the amount of pressure the presser foot applies to the fabric and the feed dogs. If the pressure is too strong, it will tend to push the upper layers of fabric, creating a bubble look. If the pressure is too loose, there is not enough pressure for the feed dogs to physically pull entire quilt sandwich under the presser foot.
(The pressure is adjustable depending on the types of fabric and thicknesses being sewn.)
http://www.sewdaily.com/how-to-sew/sewing-machine-basics/the-best-kept-secret-on-your-sewing-machine

http://makeitsew.biz/presser-foot-pressure

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Basic Tips for All

1. Always turn the handwheel TOWARDS you (counter clockwise) as turning it in the opposite direction (away from you, clockwise) may knock the timing out requiring repair from a service center.
2. Always be sure your presser foot is in the DOWN position before sewing. Sewing with the presser foot in the up position will cause your thread to tangle and your bobbin to jam.
3. Change needles regularly (after 16 hours of use) as dull/weak needles can cause damage to your machine and fabric. Only use SINGER needles on your SINGER sewing machine.
4. Always be sure you are using the correct bobbin for your machine. Class 66, Class 15 and Class 15J bobbins look very similar. However, using the incorrect bobbin class in your machine can cause damage.

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I can't see the take-up lever? h

make sure that the thread tensions are correct for the thickness of material
remember that only the bottom foot walks and draws the material through so it may need a help and be pulled as it sews.
I find that women in sewing shops just love to talk about problems and how they can help so find a shop and discuss any problems with them

sounds as if your bobbin is getting caught up not feeding right , also had some luck in past adding clear tape to cover serrated foot for finer fabrics and things like real silks and such but it has to be replaced a lot

The quilted fabric may be too thick for the walking foot to move along smoothly. Try using a zipper foot which is much slimmer and can get close to the line of stitching.

a quilting foot or buy one with a round hole in it great

check with a brother dealer about a walking foot

Do you have the proper walking foot for your machine? Make sure the pressure foot is moving up and down freely. And check to see that the feed dogs are coming up above the needle plate at least 1MM (almost as high as a dime) If they don't, remove the needle and check for any lint build up between the feed dog teeth. If they still don't come up above the needle plate, they might have to be adjusted.

Usually a walking foot is for straight forward stitching only.It keeps the many layers from shifting for you. The "hand-look" quilting takes a couple stitches forward then one back. If you look close, you will see about every other stitch is thicker and stands out more.