What is the purpose of your coin?
To make blocks verification process more energy-efficient, but still proof-of-work and also more asic-resistant. You need full blockchain, but it is not accessed whole at once. To mine block, you generate a hash and depends on this hash you need to hash it with previous block hash. But the "jump step" is bigger with each iteration. That means if you are at height for example, 1.000.000, and you have only blocks over 500.000 in memory, about 90% time you need to access that part in memory, not in hard drive, becouse the closer to blockchain height, the greater the chance of using that block. And also, it not support smart contracts (instead, transaction can have "message" field, this gives possibility to use it in 3-rd party apps) so blockchain will not be growing very fast. Empty block is about 4KB in size, each transaction is about 1KB (average). Maximum theoretical possible "jump step" is about 25.000.000 (practical even less). So, to store 25.000.000 blocks in memory (let assume that we have average 96 transactions in each block) we need 4+96 = 100KB for each block with transactions, that means 2.5 TB for latest 25.000.000 blocks. Is it a lot? For now maybe yes, but average block time is about 1 minute, so we need about 50 years to reach 25.000.000 block. In other words, after 10 years of mining we will need about 512GB of ram. It may be quite expensive to buy, but it is definitely more energy efficient (each memory module will use only about 5 watts), than Ethereum mining rig or Bitcoin asic, which are also expensive.
How many public nodes are needed and what is the current status?
As many as possible, becouse more nodes mean more stable network. To make node simply open port 10101 (TCP required, UDP recommended) download latest release form github and run. Mainnet already launched, more info on discord.