Get oracle execution plan by sql_id

So is there a way I can see the execution plan of the proc or the statement in particular?

You have to refer to DMV's for extracting such information. sys.dm_exec_cached_plans, sys.dm_exec_sql_text and sys.dm_exec_query_plan are the ones to look into.

Especially sys.dm_exec_query_plan DMF will return the plan for a given batch or procedure (along with the "subplans" for each query comprising the batch).

Note: Restarting sql server will flush out all dmv data.

Example :

-- Do not run it in PROD !!!!
-- free up the procedure cache for TESTING ONLY !!
dbcc freeproccache

-- create an SP with different queries 
create procedure usp_Kin_Test
as
select name, create_date from sys.objects
where type = 'P'
order by create_date desc

select name, OBJECT_ID from sys.procedures
order by name

-- execute the query
exec usp_Kin_Test

--- Check the DMV's for cached query plan

SELECT deqp.dbid
    ,deqp.objectid
    ,CAST(detqp.query_plan AS XML) AS singleStatementPlan
    ,deqp.query_plan AS batch_query_plan
    ,ROW_NUMBER() OVER (
        ORDER BY Statement_Start_offset
        ) AS query_position
    ,CASE 
        WHEN deqs.statement_start_offset = 0
            AND deqs.statement_end_offset = - 1
            THEN '-- see objectText column--'
        ELSE '-- query --' + CHAR(13) + CHAR(10) + SUBSTRING(execText.TEXT, deqs.statement_start_offset / 2, (
                    (
                        CASE 
                            WHEN deqs.statement_end_offset = - 1
                                THEN DATALENGTH(execText.TEXT)
                            ELSE deqs.statement_end_offset
                            END
                        ) - deqs.statement_start_offset
                    ) / 2)
        END AS queryText
FROM sys.dm_exec_query_stats deqs
CROSS APPLY sys.dm_exec_text_query_plan(deqs.plan_handle, deqs.statement_start_offset, deqs.statement_end_offset) AS detqp
CROSS APPLY sys.dm_exec_query_plan(deqs.plan_handle) AS deqp
CROSS APPLY sys.dm_exec_sql_text(deqs.plan_handle) AS execText
WHERE execText.TEXT LIKE '%usp_Kin_Test%' -- CHANGE here for your stored procedure !!

Note : You can do many cool things by digging into Plan cache as described by Jonathan here. Also refer to DMVs for Query Plan Metadata

Yes, you can specify the SQL_ID. The usage would be something like this:

SELECT * FROM table(DBMS_XPLAN.DISPLAY_CURSOR('gwp663cqh5qbf',0));

To find the SQL IDs for the current session, you'll first need to get the SID for your session, and then search v$session for the related SQL_IDs:

select sys_context('USERENV','SID') from dual;
select SQL_ID from v$session where SID='yoursid';

If the SQL aged out of the cursor cache, you may be able to find it in v$active_session_history:

select SQL_ID from v$active_session_history where SESSION_ID='yoursid';

I would recommend reading the manual page for DBMS_XPLAN to get the full details.