I think you should definently clean the cage. A dirty enviororment could be harmful to you chicken! I would clean around the nest...just dont touchh the nest or the eggs. Tell me what you did!

i wouldnt touch the eggs as your scent may be the reason for her abandoning her first egg. id look up how long it takes for her eggs to hatch and if they dont hatch for a week after they should have layed them the move both the eggs and the hen.

birds have a poor sence of smell touching and handeling the eggs will not cause a problem. since you dont know the basics of breeding it would be best if you hard boil the eggs then place them back in the cage and leave them until she abandons them also check out www.budgies-n-tiels.com and read the section on bird breeding - yes I know you have love birds not budgies or tiels but read it anyway the basics are the same