As stated by you, I'm trying to follow the schedule since a week, but could not get up at 3:00 bcz of my 8 months older daughter.. I'm doing it since 6:00 a.m and only making jap of one round of mahamantra. Today I've got very sick, suffering from fever. In such cases, how can v worship, as I couldnt bath bcz of health problem.

Concerning Your second question:

You have fever?! When i get cold and fever in the beginning stages i drink cow urine morning and evening; apply ghee to my legs and hands and inner side of my nose. Drink herbal tea for Devotees; in order to reduce the fever i drink hot water and covering my body very nicely sleep so that with perspiration comes out all toxins and infections.

But if You have a small child then You need extra help, better child will be little far from You so that he remain healthy, doesn't he?!

Yes, when we have fever better to sleep till 6 AM not to wake up early; also no need to take bath. Only hands, legs, mouth, ears, nose...but not whole body what to speak of hair.

It will help us to get healthy faster.

Worship? If You have Deities, then better to request some of Your friends or husband to do the seva for Deities. Or else if there is anyone to help then at least offer to Them some fruits so that They remain not hungry.

When we are healthy better to wake up before 6 AM. Not matter how late we slept and if we slept less hours then sleep afternoon around 20-30 minutes. It is very recommended to wake up before 6AM. 

And sleeping also we have to do on time. Or else we will loose our health. Not later than 10 PM.

Concerning waking up earlier: Maybe You can try not to eat grains for dinner but eat only subji or drink cow milk. Or some Ekadashi rice. but not grains. 

Also put alarm. And daily change the alarm for example first day alarm will ring at 6 AM the seond day and 5:55 then at 5:50 ...in this way we will easily start to wake up earlier.