How to Retrieve all possible information about a LinkedIn Account ? (API using C#)

You've already got the notation down, all you need to do is add the rest of the field selectors, nesting them where needed:

https://api.linkedin.com/v1/people-search:(people:(id,first-name,last-name,headline,picture-url,industry,positions:(id,title,summary,start-date,end-date,is-current,company:(id,name,type,size,industry,ticker)),educations:(id,school-name,field-of-study,start-date,end-date,degree,activities,notes)),num-results)?first-name=parameter&last-name=parameter

Keep in mind that per the Profile Field docs, you can only get educations for 1st degree connections of the current user.

Here is the url to get everything for a user Profile:

https://api.linkedin.com/v1/people/~:(id,first-name,last-name,headline,picture-url,industry,summary,specialties,positions:(id,title,summary,start-date,end-date,is-current,company:(id,name,type,size,industry,ticker)),educations:(id,school-name,field-of-study,start-date,end-date,degree,activities,notes),associations,interests,num-recommenders,date-of-birth,publications:(id,title,publisher:(name),authors:(id,name),date,url,summary),patents:(id,title,summary,number,status:(id,name),office:(name),inventors:(id,name),date,url),languages:(id,language:(name),proficiency:(level,name)),skills:(id,skill:(name)),certifications:(id,name,authority:(name),number,start-date,end-date),courses:(id,name,number),recommendations-received:(id,recommendation-type,recommendation-text,recommender),honors-awards,three-current-positions,three-past-positions,volunteer)?oauth2_access_token=PUT_YOUR_TOKEN_HERE

Requires an Oauth2 access token.

Here it is in a nice String list (Java):

apiUrl
    + "/v1/people/~:("
        + "id,"
        + "first-name,"
        + "last-name,"
        + "headline,"
        + "picture-url,"
        + "industry,"
        + "summary,"
        + "specialties,"
        + "positions:("
            + "id,"
            + "title,"
            + "summary,"
            + "start-date,"
            + "end-date,"
            + "is-current,"
            + "company:("
                + "id,"
                + "name,"
                + "type,"
                + "size,"
                + "industry,"
                + "ticker)"
        +"),"
        + "educations:("
            + "id,"
            + "school-name,"
            + "field-of-study,"
            + "start-date,"
            + "end-date,"
            + "degree,"
            + "activities,"
            + "notes),"
        + "associations," /* Full Profile */
        + "interests,"
        + "num-recommenders,"
        + "date-of-birth,"
        + "publications:("
            + "id,"
            + "title,"
            + "publisher:(name),"
            + "authors:(id,name),"
            + "date,"
            + "url,"
            + "summary),"
        + "patents:("
            + "id,"
            + "title,"
            + "summary,"
            + "number,"
            + "status:(id,name),"
            + "office:(name),"
            + "inventors:(id,name),"
            + "date,"
            + "url),"
        + "languages:("
            + "id,"
            + "language:(name),"
            + "proficiency:(level,name)),"
        + "skills:("
            + "id,"
            + "skill:(name)),"
        + "certifications:("
            + "id,"
            + "name,"
            + "authority:(name),"
            + "number,"
            + "start-date,"
            + "end-date),"
        + "courses:("
            + "id,"
            + "name,"
            + "number),"
        + "recommendations-received:("
            + "id,"
            + "recommendation-type,"
            + "recommendation-text,"
            + "recommender),"
        + "honors-awards,"
        + "three-current-positions,"
        + "three-past-positions,"
        + "volunteer"
    + ")" 
    + "?oauth2_access_token="+ token;