Engineering Entrance Exam

Yes, there are no restrictions on students to prepare for JEE provided they fulfil the criteria for JEE exams. The eligibility for JEE is as follows:
Basic eligibility:
Nationality: Candidates must be an Indian citizen.
NRIs, PIOs, OCIs & Foreign national candidates can also apply.
Number of Attempts: Candidates can apply for JEE Mains exam only three times. This attempt limit will be counted from 2017.
Aadhaar Card is compulsory to apply for this exam.
Age criteria:
Age limit: Candidates whose date of birth falls on or after 1st October 1993 (for general and OBC candidates) are eligible to apply.
Relaxation: If candidates belong to a reserved category like SC, ST and PwD category then the date of birth falls on or after 1st October 1988 are eligible for JEE Mains.
Candidates note down that the date of birth mentioned in the Secondary Education Board/University will be considered only for appearing in the exam.
Qualification criteria:
Qualifying exam: Candidates must qualify their 10+2 or equivalent examination from a recognized board.
Subjects: Candidates must have to take a minimum of 5 subjects in 12th/equivalent examination. Candidates appearing for JEE Mains 2018 must have passed class 12th with Physics, Chemistry & Mathematics in order to apply.
Passing marks: There is no prescribed percentage to appear in the examination. Candidates having passing marks can also apply.
Only for admission to NITs, IIITs and CFTIs, candidates should secure minimum 75% marks (65% for SC/ST students) in the qualifying examination or must be in the top 20 percentile in class 12th examination conducted by the respective boards.
Appearing candidates: If a candidate appears in class 12th or equivalent class in 2018 then he/she is also eligible for JEE Mains 2018.
NIOS candidates can also apply for this exam.
Diploma holders: To appear in JEE Advanced, a Diploma holder can apply in JEE Mains 2018, but their rank & score in JEE Mains will not be considered for admission in NITs & CFTIs.
No board marks will be taken into account for calculating JEE Mains score from the year 2017 onwards.

It is good that you have taken the initiative early. That shows your enthusiasm. Now that you have decided to take the test you must reflect the thought "Why exactly do I want to write GATE?"
There are two perspectives to that question-
1. Decent score to get a good job
2. For further studies and if you are interested in research, it will be a good start.
Since you are in your second year, try joining an institute for guidance and attend the classes. Prefer going to the crowded ones for a better GATE score and low understanding if you want an immediate job.
(Or)
Go to a private tutorial who have less number of students and give more specific interest in feeding in the basics or the base of fundamental engineering. Here you will learn how things work instead of mugging up formulae.
Try searching for applications on your smart phone or laptop that keeps you updated about the exam. Believe me there are lot of such applications.
Although still in second year I wont recommend you to waste time in interesting yet not so important topics in your curriculum
Now these points that I mention will be of utmost importance.
1. Take down the syllabus of your specified course and stick to the syllabus.
2. Make sure you make one and only one notebook per subject, lets say its the fair notebook and you must keep it as a relic. Whatever you enter into this notebook should be very important points and no rough work or rubbish. Keep a rough note too to do those things.
3. Start watching videos from NPTEL. Its free and the best as far as I can go.
4. Once you start doing it enrol in a class and always attend it. Never miss a class.
5. Go slow take your time you have plenty of it.