Is there a risk of falling on wet flooring especially near the sink and washing machine?

Non-slip mats, a fitted carpet or carpet tiles could be used.  Wet floor areas should be mopped as soon as possible.

Is everything within easy reach without stretching or climbing on chairs/stools etc?

Stretching and reaching above head height can make you feel dizzy and there is a temptation to climb up on chairs to reach something. Things, which are used regularly, should be on the ‘easy to reach shelves’.

If steps have to be used, are they secure with a handrail and system to keep the legs locked?

Never use a chair or a stool to stand on. Properly designed steps can be used in reasonable safety if you are fit enough. They must be designed with an effective handrail and with an easily applied lock for the legs. If possible, ask someone else to help.

Do you struggle to carry items from the kitchen to dining area?

You might benefit from a kitchen trolley. Trolleys are not recommended as a walking aid,  they are to carry items from one place to another. If you are unsteady on your feet you will need an assessment to see if a trolley is safe for you to use.