There are too many questions that ask for too many explanations, I don't think anybody wants to answer to all that. It is not really possible to give a "very basic without technical term" definitions to most of these words. If you want to write an article in mathematical biology, I am afraid you will have to take some time to learn a bit about biology. Go through some books that will guide in the basic understanding of biology. I know we all would like things to be easy when starting a new field but unfortunately there is no easy answer to your questions. This book for example might help you. It is a classic in first year Bachelor in biology.
If you have some specific questions, you are very welcome to ask them. But this post asks for a whole book!
Here is a small quickly written text that will maybe help you a bit. Note: it might be oversimplified sometimes!
DNA is a big molecule made of (among other things) nucleotides. There are 4 nucleotides (adénine, cytosine, tyrosine (or Uracile on RNA) and guanine often just called ACTG and they can be categorized in two types of molecule depending on their number of cycles) which sequence form the genetic information. DNA, in eukaryotes (which are cells that contains DNA in a nucleus (which is the case of all non-virus, non-bacteria and non-archaebacteria)) is grouped into chromosomes (which are usually represented by a "X" as they more or less appears at the metaphase (a phase during the life cycle of a cell)).
DNA is transcribed into mRNA (a kind of RNA) which is then translated into protein (by rRNA and tRNA). While RNA and DNA are made of nucleotides, the protein is made of amino acids. Three nucleotides (one codon) codes for 1 amino acid.
In the genome there are sequences that code for proteins, sequences that code for RNA, sequences that allows other proteins to bind into in order to influence gene expression, promotors, enhancers… You will have to accept taking some time learning a bit about that stuff I guess.
Sequencing is the (artificial) process of reading a DNA sequence. This can be achieved on a whole genome or on small chosen sequences.
As the nucleotides G binds only with C and A binds only with T (two nucleotides together form a base pair)(there are two strands of DNA linked by the nucelotides), the amount of G equals the amount of C and same for A and T. The GC content gives the proportion of G and C of the total number of nucleotides of a sequence (or a whole genome). Oh by the way, a genome is the totality of the DNA of a given individual.
Positive/purifying selection are cases of natural selection. Natural selection is a process by which the frequencies of alleles (variant of a gene) does not vary randomly. They vary according to the reproductive success (= fitness) they confer to the individuals that bear the allele. Positive selection on an allele means that this allele is selected for. Purifying selection refers to the wildtype allele (most frequent allele) is selected for and all mutations (DNA modifications) that appear are deleterious and therefore counterselected,
A SNP is a genetic variation between individuals in a population (or along populations or species) that involves only one nucleotide.