Recently I have started my period but the problem is the blood comes in small amounts once a day and the rest of the day is light discharge. Is it valid for me to still both fast or pray?
No it isn't and it is rather a sinful act unless you see no blood, but a "white discharge".
Read for example:
"Women used to send little boxes to A'isha, umm al-muminin, with a piece of cotton cloth in each one on which was yellowness from menstrual blood, asking her about the prayer. She said to them, 'Do not be hasty until you see a white discharge." By that she meant purity from menses. (Muwatta' Malik)
And here is an explanation of the stages of menses:
Al-Nawawi (may Allaah have mercy on him) said: The sign that the menses has ended and the woman has become pure is when the bleeding and yellowish and brownish discharge stop. When that stops the woman becomes pure even if some white discharge comes out after that or not. End quote from al-Majmoo’ (2/562).
And this hadith shows that you are not allowed to fast:
... He said, "This is the deficiency in her intelligence. Isn't it true that a woman can neither pray nor fast during her menses?" The women replied in the affirmative. He said, "This is the deficiency in her religion." (sahih al-Bukhari)
however you'll be asked to make up your fast. You also are not allowed to pray, but won't need to make up your prayers for the time of your menses. Note that even if you didn't perform ghusl after becoming clean from your menses you are asked to fast!