Hi, thanks for answering the questions. I do see a few things that could be tributing to her symptoms. You mentioned that you're using a thermometer like they use in hospitals but that way of checking temps wouldn't be accurate so the temps could be quite a bit off. The only 2 ways to get an accurate reading are with either a temperature gun or a digital thermometer with a long wire & probe on the end like this:
You can find one of these digitals at Walmart for about $12.00 and would be in the area where the outdoor plastic thermometers are sold. They are well worth the investment and it's very important that you find out what the temps really are because babies won't do well with incorrect temps. Babies tend to like temps quite warm so a little over 100 (38 celcius)and up to 110 (43 celcius) would be good temps for him but please don't make any adjustments until we find out the size of the tank and you get an accurate thermometer.
That's good that you're using reptile carpet on the bottom. Could you tell us what size tank you're using the 150 watt basking bulb in because that is a high wattage bulb and just want to make sure that it isn't a 10 or 20 gallon tank as that would cause overheating and dehydration.
Unfortunately, there have been some health issues associated with the Repti-Glo 10.0 fluorescent bulb causing lethargy, eye problems and others. The safest way to use that bulb until you replace it in about 5 to 6 months is to have it 10" from your beardie and alongside a bright white basking bulb. How close has that bulb been to your beardie? I think this bulb is another problem as well as the temps.
Dandelion greens are a good staple food but kale shouldn't be fed daily and carrots shouldn't either. Lettuce really doesn't have any nutritional value for a baby and is mostly water. Here's a site that most of us refer to:
http://www.beautifuldragons.503xtreme.com/Nutrition.html The daily staple foods are printed in green ink and it also tells what foods to avoid.
Are you using calcium and vitamin supplements, if so, how often and what brand? That's good that you've been syringe feeding him, has he been licking it off his nose or have you had to forcefeed it?
What veggies are you using? Keeping him well
hydrated is a good idea.
Please fill us in on the other answers and we can go further, we need to help get him improving.