Use a Fuller bit to drill for deck screws. Install one at a time. No need to remove old fastener. No need to plug if carpeted over. Just set the screw flush.
Wrong bit for a construction or deck screw. It's only appropriate for old school wood screws which are not correct for flooring. That bit is made for a tapered screw shank, only traditional wood screws are of that design and they will eventually back out in a flooring application.
Bit is also fragile and worthless at chip extraction, will break unless extreme care is exercised in it's use. I've used them extensively in furniture construction but this is not the place for them. No need for a countersink in this instance as the screw will sink itself flush and that's what is desired. It needs to be tight - very tight. This is construction, not building cabinets. Use the appropriate fastener and all is good. If you insist on pre-drilling for deck or construction screws, then use a straight bit appropriately sized.
BTW, you do need to remove the old fasteners if you want to eliminate all squeaks. It only takes a few thousandths of movement relative to the old fastener to squeak. The wood surrounding them has dried out and shrank away from them leaving them loose in their holes. That is where the squeak originates. Many times those original nails are rusted due to exposure during construction or pet urine or spills over the years. The rust just exasperates the squeak problem. If you want to chance a squeak after you install your expensive carpet, hardwood, tile or laminate flooring - go ahead and leave the old nails - if you don't want a squeak to return, pull the nails and put the screws in their place.
