I think you need pulls. On the unit to the right of the stove, have the pull in the centre of the top rail if it's a cup pull or vertically in the centre of the door panel if it's a long pull. The cabinets look unfinished without hardware. You may want to consider putting knobs on the upper cabinets as it will help break it up a bit and provide some visual interest.

Goof luck.

Hardware helps to prevent grime, oils and food from collecting all over your cabinetry so use handles. Choose handles of all the same size. For safety and ease of use I recommend choosing handles that are rounded and have no open ends that can snag clothing and tear it. The types that will work best with your cabinetry include Rejuvenation's mission drawer pulls, offset drawer pulls, mission d pull with backplate, classic cabinet pull and rustic cabinet pull. The pulls enable the elderly, and those with grip or shaking issues such as those that come with Parkinson to easily open and close the cabinets. I would choose a darker finish which will make it easier for individuals with vision issues to see the handles. If you have children or children visit your home these types of pulls make it easier to use child cabinet locks on them. You can install the pulls sideways for door handles. I hope this helps you.

The purpose of hardware is to protect your cabinets. Over time, the oils from your hands will disintegrate the finish and leave grimy marks that are tough to fix. Many Americans redo their kitchens every few years, but your cabinets are traditional and will stand the test of time if you decide to keep them a good while longer.

you could paint the cabinets white with silver handles

To answer your questins..
1 Yes! it will increase the life of your cabinets.. Oils from hands plus soap from cleaning hand prints will tear down your varnish and increase the natural bio degrading of wood.
2. It would be wise to use the same size due to the fact you might want to change to a more modern style in 8-10 years or the next owner might want to change and trying to find a set that matches every size you put in would be miserable. It is alright to do knobs with pulls and mix it up by putting knobs on doors and pulls on door or vice versa..
Either way if you do pulls, keep them all the same size.

For super contemporary kitchens with really wide drawers.. the really wide pulls look awesome.. That just isn't the case in this kitchen. You will also find really wide pulls are 3 times or more than the cost of a standard size pull.

You can do a mix of knobs and pulls, but keep them consistent in size, placement and door type (do knobs for all doors and pulls for all drawers, for example). The size of the knob/pull is your preference. I like to tape up a piece of construction paper that is the size and shape of whatever ones I am considering, to test for size and location. Make sure you don't have to stretch or bend down to open them.

Personally, I dislike all hardware on kitchen cabinets. The reason is simple. It's a royal pain to clean around the hardware. If it were a nice flat surface, no problem to wipe down.