The Likert scale I am analyzing has both positive and negative questions, but all the items are answered with 4 - strongly agree, 3 - agree, 2 - disagree and 4 - strongly disagree. For analysis, should I make the weight of the answers the same?
For example, if the statement is positive, then 4 must be given to strongly agree, and then for negative statements, a 4 should also be given to strongly disagree. What else can I do aside from Mean and Standard Deviation?
There are two things that one shouldn't mix. Positive/negative wording of an item and positive/negative anchoring (or orientation) of an item to the scale (the construct). Consider, for example, construct "Religiosity". Items are all rated by 1 = strongly disagree to 4 = strongly agree. "I do not believe in the evolutionary theory" is a negatively expressed statement agreement with which adds you scores on Religiosity. "I seldom or never visit church on Sunday" is an item reversely anchored to Religiosity: if you strongly agree with the statement, you should revert its rating scale and add 1, not 4, to Religiosity sum.
[Not]"I seldom or never visit church" gives clue for reader to know that the rating scale was reverted. And, of course, test documentation must make it clear in what direction each item is anchored to the construct.
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I would recommend reading Agresti's work (e.g., "Analysis of Ordinal Categorical Data") as a starting place for Likert scale data.
I provided an answer this type of question here. I give direction to jMetrik software: https://itemanalysis.com/jmetrik-4-user-guide/
One of the classic texts on this subject that is relatively easy to follow is:
Crocker, L.M., & Algina, J. (1986). Introduction to classical and modern test theory. New York: CBS College Publishing.
"What else can I do aside from Mean and Standard Deviation?" <- Design your survey in a way that tests for internal reliability. You can switch the direction of the scale to test for alertness. If people are just doing quick checkbox answers and think that they have a pattern in the scoring, then they might be lazy and check 10, 10, 10, 10 while thinking that they strongly disagree the whole way through. You want meaningful data. This is where jMetrik and the associated statistics provided by that software has it's use. It gives you the opportunity to examine the quality of your survey.
Once you have a well designed survey you can begin to generate survey statistics. Cronbach's alpha is an important statistic that you want to look at. It is used to estimate the internal reliability of the survey questions. It is also called a reliability index. You can use the jMetrik software that I linked too or you can do this kind of analysis using the r-stats psych package (https://www.r-bloggers.com/five-ways-to-calculate-internal-consistency/). More details on Cronbach's alpha is posted Here.
Another way to improve on your survey data is to break the questions into themes. You can then statistically examine for differences in responses of main themes. For example, these questions are all about technology while these questions are about nature. Is there a significant difference in the scores between questions that focus on technology relative to those that are nature themed? This is where you can start to explore t-tests or ANOVA's, but it requires lots of consideration in the way that design of your survey.
The following paper provides an excellent tutorial:
Hinkin, T. R. (1998). A brief tutorial on the development of measures for use in survey questionnaires, from Cornell University, School of Hotel Administration https://scholarship.sha.cornell.edu/cgi/viewcontent.cgi?article=1515&context=articles
