When I have a broody I establish a routine before she is allowed real eggs.
1. I settle her into her broody coop and run for 12 hours shut in.
2. She then has two or three days sitting on crock eggs, just to make sure she's not kidding about this broody business.
3. During step 2 I lift her gently out of her coop twice a day (morning and mid afternoon) and close the coop behind her. She will then have free access to mixed corn and fresh water. Often broodies have a bit of a panic and are desperate to get back to their eggs without eating or drinking. Be patient, don't' forget they are only crock eggs at this stage. I like to sit on a chair quietly near her coop and run so she starts to associate me with 'being out time' and won't panic as much once her chicks are hatched if I'm around them.
Once she has had a good drink, feed, poo (formed at the GATES OF HELL!!!) and scratch around (5 minutes or more) I open the coop again and she will return to her crock eggs. Clear up her large firm poo and fling as far away as possible. this will mean that her run will stay fresh for when the chicks arrive and she'll not track through the poo on subsequent perambulations and track it back onto her eggs.
4. Once the routine is established I then swap her crock eggs for real eggs and keep the routine up until just before hatch date. Then just leave her be.
5. Leave her coop door open during the day so she has good daylight and shut her in at night but of course keep her and the coop well shaded from hot sun and sheltered from the worst of bad weather.
6. The only addition to this is if the weather is cool or inclement I place and old folded hand towel over the eggs while she is having her constitutional.
My only comment about your broodies runny poo is that she might be a bit out of condition. Being broody is hard work and she has no time to be herself. Make sure she is only eating mixed corn, not layers or other treats etc. However you could possibly offer her a good dollop of live yoghurt mixed into some uncooked porridge oats to help her 'happy' bacteria in her gut and add a small dash of ACV to her water.
Hope this helps.
Orchardlady.