Can't see the 3.99% rate you are talking about. The only thing you may be looking at is a remortgage that is a 3 year fixed rate at 4.99% and then onto the variable rate which is currently 3.99%. This is listed as the top product in the 90% range but the rate your mortgage will intially be based upon is 4.99% and not 3.99%
The only thing I can see in the "low deposit" tab is a 4.19% 2 year fixed (still better than the product I quoted). What would concern me though is that you would not be placing a deposit but using equity to decide your product...although they are much the same thing they are used for different products. The only difference would be that you would use a deposit to buy a house and so would use it on a purchase mortgage where as you would use the equity in your house to remortgage and I think that the products in the Low Deposit tab are for purchase only and that will make a big difference....if only for the associated fees to be paid.
Quite often you will find that the same product is available for remortgage and purchase but the only difference will be that the lender will often pay for the legal work and for a valuation as part of the package where as for a purchase you will normally have to pay for this yourself, all told it will likley save you around £700 - £1000 for a remortgage over a purchase for exactly the same product.
To answer your other question. Fixed means exactly what it says. When you fix your rate it remains at the same rate from start until the promotional period is over....ie. 2 year fixed, 5 year fixed. During this time if you have a rate of 3.99% then your mortgage will be charged at that rate.If there are interest rate rises and the rate goes sky high, your a winner, if it drops you stand to lose out...it's the risk you take but it is the safe bet if you are watching the pennies so that you can control your budget knowing exactly what is going out eagh and every month for the next 2 or 3 or 5 years depending on what period you opt for.
Be aware that the longer you fix your rate for the higher it will be. 2 year rates are always the cheapest rates.
Good Luck.