Having recently flown - yes, one item including handbag, so unless you can stuff your handbag in the hand luggage, you can't take both. If you do, the bag goes in the hold and you will be charged even more for it, and you might be over your luggage allowance.
Five items of less than 100ml in the clear plastic bag. However - if you don't take those things through security, but buy them in the chemist in the departure area after you've been security checked, you can still take them on board. We take mini sizes of shampoo, deodorant etc., which you can buy in Boots or Superdrug, no need to take huge pots. A mini size will easily do you 2 days.
As long as your hand baggage fits in the metal sizing frame at the airport (size as per grasscarp's post) it will go on board ok.