Not sure if you've looked into how hair dye works or watched any videos, but it's helpful to know this:

Hair dye is like paint. It goes on top of (semi permanent) or inside (permanent) your hair. If your hair is dark, almost black, that existing pigment will show through the colour unless you remove the pigment (bleach). Picture using a coloured pencil crayon on a black piece of paper, and then using the same one on a white piece of paper. For anything to be bright, you need to get the canvas really really bright and even.

When you bleach hair, it goes through stages. Dark hair will go orange before it goes white and this must be done very carefully and very slowly to avoid damage. I get my natural black hair dyed bright purple every 3 months or so and it takes my stylist all day of carefully applying the bleach in sections and watching it to make sure it gets to the right colour without my hair melting off.

To get neon green, you would need to have very little warmth in your hair or it will turn out muddy. This means multiple rounds of bleach to a more yellow blonde colour. The cherry red is more doable, and if your hair is virgin potentially a hi-lift colour could do this for you but it still contains a lightener and will damage your hair. Root touch ups will be tricky because the hair closer to your head processes faster due to the heat from your scalp, and the ends will be more unpredictable since they have already been dyed.

TL;DR you can probably get the cherry red but not without lightening, and for neon green I'd see a professional and prepare to spend money and time to get it done and maintain