First of, i'm not from electronics background, i'm sorry if my question sounds stupid or irrelevant. I recently started a project as a hobby with a help of https://www.mysensors.org/build/irrigation i have purchased all the components and has built the circuit half way but i'm stuck at what kind of power adapter should i use i currently own a mobile adapter with output of 5V 350mA. But the Absolute ration of Arduino Pro Mini is 200mA as per How much current can I draw from the Arduino's pins? Is it possible to use a 5V 350mA DC input to my chip ? Or would it burn off my chip? if so what kind of adapter or a current regulator should i use ? A current regulator circuit would be much appreciated.
Your power adaptor can supply UP TO 350 mA. It does not force that current into any connected load.
The Arduino will draw whatever current it requires, when given an appropriate power supply voltage.
If the arduino plus whatever else you add to the circuit requires more than 350 mA, the power supply will be overloaded, and its output voltage may drop, or it may be damaged.
The project you are working on does include a sizable 8-channel relay board. The board, according to its picture, uses SRD-05VDC-SL-C relay. Each 5-V relay needs 90 mA of current to work. If all eight are engaged, you will need a 5-V power supply with at least 720 mA capability, plus whatever the Arduino/radio/display need to take.
BTW, absolute maximum ratings for Arduino (200 mA) has little to do with actual consumption, it will be much less than that in your case. But it would be safe to budget in these 200 mA. So, you have to incur one more expense and buy a better 5V AC-DC adapter with at least 1A rating, better get a standard 2-A - 2.4-A, from any surplus store.