Perlite is a substrate used to improve drainage and keeps the soil from compacting as quickly as it would without. Mg alone is too water retentive. Your buckets may have good drainage but the soil used for containers also needs to drain well. It's really too late this year to do anything about the soil but you will know next time. Get a water soluble fertilizer with the numbers 10-10-10 or something similar and follow the mixing directions. Then you can either water with this solution every 4-6 weeks or mix that equally with 3 more gallons of water and water with that every time you water.

Because you started them indoors you will need to harden them off before you set them outside (do a search on this forum for hardening off, there are a lot of great threads). Radishs do not like to be transplanted and you should direct sow them. I would pitch the ones growing now and start new when the threat of frost has past. Same with the beans. You will need shop light to keep the happy inside, just light from a window is not enough. There are lots of other threads on seedling set-ups, all include lights. I hope that helps Keriann~

Radar, that is GREAT news! I am SO happy for you! (To answer a question that you had asked previously: temps in the 40s will have no effect on seedlings. I have mine outside year-round except when there will be a hard freeze. Bulbs in the ground with some mulch can easily tolerate a freeze, but bulbs planted in pots or seedlings in trays cannot. I also bring them inside if there is a threat of frost. Otherwise, outside under the large oaks. Happy, happy, happy. For anyone reading this forum regardless of zone, if your weather is beyond threat of freeze or frost, try putting your bulbs and seedlings outside in a lightly shaded area. You won't believe how well they do. Carol

Thanks guys! Replying to both comments: 1) Yes they look better on camera than in real life. I did not test soil, it's a part of routine fertilizing I do every year, didn't have problems before, applied according instruction 1 cup per 10x10 ft. There were high winds along with storms, very high winds I'd say, like 50+ mph. 2) I use castile soap diluted in water 5 tbsp per 1 gal. Thanks!