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Here is a great article to explain the process to you.

https://www.gardeningknowhow.com/edible/vegetables/vgen/straw-mulch-for-vegetables.htm

Here is some tips that work for me!

Start seeds in seed starting cell trays. Depending on the type of seeds 1 to 3 seeds per cell.
Use a seeding starting soilless mix. It needs to be light so the seeds can germinate and grow lots of roots to help in repotting.
Don't move the seeds up to pots to soon! Let them develop lots of leaves and roots. Patience.

When I move from starter cells to a new pot I only go to a 3 inch pot. Use the same soilless mix and continue to care for them.
Keep them in this size pot until it also is quite large and full of roots, now you are ready to go to the garden or approx 6 inch pot size and regular good quality potting soil!

Search our site for growing information for specific seeds and plants.

Here are some links for you.

https://www.gardeningknowhow.com/garden-how-to/seeds/when-to-start-seeds.htm
https://www.gardeningknowhow.com/garden-how-to/seeds/leggy-seedling.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soilless-growing-mediums.htm
https://www.gardeningknowhow.com/garden-how-to/seeds/soilless-seed-mix-info.htm

Minerals or contaminates in the water are likely being absorbed into the perlite.
Often times if the water has a high iron content it will collect on the perlite and appear as the orange-red color that you are seeing.

You also could have some fungus growing on the soil surface.

Making sure you have some amount of airflow around the seedling area can help curb fungus growth.

I like to run a small fan near the area of my seedling trays for a few hours a day. The air movement helps prevent excess moisture from forming and makes for good strong seedlings.

Remember to use good, sterile, soilless mix for seed starting and clean potting cells. If you reuse pots always wash them in a mild bleach solution prior to planting.

https://www.gardeningknowhow.com/special/containers/how-to-clean-containers.htm
https://www.gardeningknowhow.com/garden-how-to/seeds/soilless-seed-mix-info.htm

Here is a link to a vegetable planting guide that will tell you the ideal temperatures for transplanting seedlings in your garden:
http://extension.oregonstate.edu/deschutes/sites/default/files/Horticulture/documents/soiltemps.pdf
The first step is determining if your seedlings are truly ready to be transplanted into your garden. The article below will assist you with that determination. The general rule of thumb is that when a seedling has three to four true leaves, it is large enough to plant out in the garden.

https://www.gardeningknowhow.com/garden-how-to/seeds/when-to-transplant-a-seedling-plant-into-the-garden.htm

When the seedlings are ready, they need to be "hardened off". The article below will explain the hardening process. Basically, hardening is a process where you get your plants acclimated to outside temperatures before you place them in the ground.

https://www.gardeningknowhow.com/garden-how-to/seeds/how-to-harden-off-your-seedlings.htm

The time to prick out seedlings can vary with they variety of seeds that you are growing.
A good guideline is when the seedlings have developed at least 2 sets of true leaves.
Here are some articles with tips on seedling care.
https://www.gardeningknowhow.com/garden-how-to/seeds/seedlings-after-germination.htm
https://www.gardeningknowhow.com/garden-how-to/seeds/how-to-harden-off-your-seedlings.htm
https://www.gardeningknowhow.com/garden-how-to/seeds/leggy-seedling.htm

I have used heating pads for years to help encourage seeds to germinate in my home. I understand your concern, and even now it it is difficult to find a heating pad that stays on; most that they sell now have a built in timer and shut off after a period of time, they also do not get as warm as 'they used too'.
If you want to ensure the temperatures and germination I would suggest you go ahead and buy a seedling heating mat. They are available at most garden centers and greenhouses. They may cost a bit more, but have a temperature regulator on them so you can keep the temperature constant.